The concept of "moral entropy" appears across theology, information ethics, sociology, and popular discourse, yet no existing account provides a unified structural mechanism for how moral reasoning degrades, a severity metric for classifying that degradation, or an explanation for why some moral damage resists repair while other damage does not. This paper presents such an account through the framework of Resolution Ethics (RE). RE identifies deception (self-deception and other-deception) as the singular corruption source through which the Protection, Trust, and (...) Free-Agency (PTF) architecture between agents degrades. Moral entropy is the accumulated result of that degradation in the relational field: repeated or critical corruption of the PTF structure, traceable to deception as its source. (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the (...) most important notions of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

This paper formalizes the concept of Narrative Entropy as a quantifiable metric for assessing structural disorder and informational friction within literary and cinematic systems. While the term finds its roots in Shannon’s Information Theory and Pynchonian metaphors, this study defines it as a core component of the Objective Projection methodology. By analyzing the tension between causal predictability and structural chaos, we establish a parametric framework for Narrative Engineering, allowing for the mathematical modeling of story progression.

Based on Lao-Yang Genesis Cosmology, this study proposes a rigorous law of hierarchical cosmic evolution: Human follows Earth; Earth follows Heaven; Heaven follows Dao; Dao follows Nature, and establishes the physical energy and feedback chain of Dao generates One (the Sun), One generates Two (the Earth), Two generates Three (the Moon), Three generates all things. -/- The central argument of this paper is that the cyclical systemic collapses and disasters of Chinese civilization over the past two millennia (such as the (...) fall of the Ming dynasty and the Great Leap Forward famine) are essentially the result of a subjectivist philosophy centered on the “sage,” which forcibly reversed the natural flow of energy and information. By attempting to replace “Human follows Earth (empirical physical reality)” with “Human follows Self (subjective will),” it induced a fatal form of “Sage Entropy” within the civilizational system. -/- The study deconstructs Zhang Zai’s clan-based cosmology and Wang Yangming’s “Mind-ism virus,” arguing that they reduced the grand galactic logic into humble ethical dogma, thereby severing civilization’s connection to the 1-2-3 physical constant system. The paper further analyzes Maoism as a radicalized manifestation of “Sage Entropy,” demonstrating that the doctrine “Man must conquer Nature” constitutes, in essence, a violation of the Second Law of Thermodynamics and the energetic limits of photosynthesis. This subjective tampering with natural hierarchy led to feedback deadlocks within the bureaucratic system and social heat death. -/- In response to this civilizational pathology, the paper proposes a restart path grounded in the Way of Nature: repositioning humanity at the end of the Earth–Heaven–Dao chain through cognitive reset; replacing “standard answers” with “experimental friction” in educational reform to extinguish the ghost of subjectivism; and constructing a “Digital Heavenly Dao” algorithm aligned with galactic nonlinear logic. -/- The study predicts that civilization’s redemption does not lie in seeking a new sage-king, but in acknowledging the humility of human will and reconnecting to the universe’s negentropic flow. Only by following the 1-2-3 Genesis Law can Chinese civilization transcend the cognitive bottleneck of the 21st century and enter the era of galactic evolution. (shrink)

Claude Shannon's 1948 entropy formula H = −Σ pᵢ log pᵢ established the mathematical foundation of information theory, quantifying uncertainty in discrete symbol distributions within communication channels. This paper introduces Narrative Entropy (Sn), a formally distinct but epistemologically related metric developed within the Bulut Doctrine framework, which measures the dynamic accumulation of cognitive resistance and structural uncertainty across the temporal dimension of narrative experience. We demonstrate that while Sn draws its foundational intuition from Shannon's H, the two metrics (...) differ across six critical dimensions: domain, temporal structure, measurement object, operational unit, directionality, and engineering function. Sn is not an application of Shannon entropy to literature — it is a structurally independent metric that addresses phenomena Shannon's framework was not designed to capture. We further demonstrate the relationship between Sn, Narrative Gravity (Ng), and biophysical reader output, and provide benchmark calculations for Crime and Punishment, Moby Dick, and Pulp Fiction. (shrink)

Narrative Entropy (Sₙ) is a structural-complexity construct of the Bulut Doctrine that quantifies the cognitive resistance and causal uncertainty a narrative imposes on a reader across time. Because the construct has been developed incrementally across the corpus, its operational expression has appeared in more than one form. This technical note serves a single purpose: to fix, in one place, the canonical definition of Sₙ, to document the version history of its operationalisation, and to state plainly the one open formal (...) problem that remains unresolved. -/- It makes no new empirical claim; it is a reference and disambiguation document, not a validation study. The canonical general form is the time integral of the product of Information Friction (If) and Causal Branching (Cb): Sₙ = ∫ (If × Cb) dt. The product form Sₙ = If × Cb × t used in the registered pilot is its scene-constant special case. The known dimensional inconsistency of the product form — both If and Cb being per-minute rates — is documented here as an open question, consistent with the pilot report that first recorded it. The note also includes the full version history of the measurement protocol (v1.0 normalised anchors → v2.0 raw rates), the two worked pilot examples for reference, and the formal distinction between Sₙ and Shannon entropy. -/- Keywords narrative entropy, Sn, Bulut Doctrine, Objective Projection, narrative engineering, operationalization, information friction, causal branching, version history, canonical definition, Shannon entropy. (shrink)

This book is a critical monograph on the problem of Chinese intellectuals, grounded in the philosophy of science as methodology, thermodynamics and complex systems as analytical tools, and the Lao-Yang Genesis Cosmology (LYGC) as its ontological foundation. The title concept, Sage Entropy (圣人熵), names the book's core original contribution: the ontological error of Confucianism — substituting the subjective will of sages for the laws of the cosmic natural order — accumulates irreversible thermodynamic entropy within civilizational systems, driving the (...) periodic collapse of civilization and the desertification of thought that has recurred across two thousand years of Chinese history. The structural logic of the book follows a seven-layer chain of deduction: Artificial Order Is False (ontological verdict) → Sage Entropy (thermodynamic mechanism) → Knowledge-Power Conspiracy (institutional logic) → Intellectual Desertification (cognitive result) → Civilizational Decline (historical evidence) → Dao Follows Nature (cosmological way out) → Reconstruction of Natural Civilization (practical program) — The Seven-Layer Core Deductive Chain of This Book -/- The book is divided into seven parts (including the Prelude and Part Six, the Constructive section), comprising twenty-five chapters in total, with Appendices A through G and a bibliography. Summary of Each Part -/- [Prelude] Drawing on the Guodian Chu Slips (unearthed 1993), the Mawangdui Silk Manuscripts, and the Taiyi Shengshui as archaeo-philological evidence, this section argues for the Chu civilizational roots of Laozi's thought and establishes a documentary foundation for the LYGC cosmology reaching back two and a half millennia. [Part Zero: Ontological Premises] Using the LYGC cosmic hierarchy (humanity follows Earth → Earth follows Heaven → Heaven follows Dao → Dao follows Nature) as a normative baseline, this part systematically argues that Confucian artificial order (the Five Constants of ren, yi, li, zhi, xin plus the Three Bonds and Five Relationships) constitutes a fourfold subversion of the cosmic natural order: epistemological subversion, hierarchical subversion, energetic subversion, and subversion of knowledge production. [Part One: Diagnosis] A historical-institutional pathology: how Emperor Wu of Han's exclusive promotion of Confucianism established the institutional origin of intellectual serfdom; how the 'system overfitting' of the imperial examination system mass-produced cognitively domesticated intellectuals; why three waves of enlightenment (late Ming/early Qing, May Fourth, the 1980s) each ended with national salvation suppressing awakening; and the contemporary academic degeneration revealed by Li Bozhong's data, alongside Chinese universities' DeepSeek ambitions and DeepFake illusions. [Part Two: Critique of Confucianism] Deconstruction at the level of philosophical ontology: the verdict on the nature of the Five Constants under the proposition 'Artificial Order Is False'; the strict operational definition of Sage Entropy (dS/dt = ρ_r · DAF / ΔCCF) and its historical verification; the structural co-option mechanism behind the myth of 'Confucian-Daoist Complementarity'; and an ontological critique of Tu Weiming's New Confucian thesis of 'Mind as Ontological Foundation.' [Part Three: Roots] The ABCDE five-factor framework for civilizational failure, arguing that A (Confucian artificial order) is the core variable but not the sole one; an extended analysis of the Qian Xuesen case through engineering cybernetics; the Guo Moruo case; and a unified thermodynamic explanation for intellectual degeneration. [Part Four: Comparison] A comparison of the University of California system (self-organizing dissipative structure) versus Confucianized universities (heteronomously organized ritual coercion); an institutional analysis of Chen Yinke as the solitary historical witness to Chinese intellectual independence; and the third path offered by Laozi and Foucault. [Part Five: Transition] The naturalization of scholarship and the university: the convergence of Liang Qichao's 'academic independence' with Dao Follows Nature; a true ontology of the university; and the only possible path for Confucianism to be reborn within the framework of the Natural Way. [Part Six: Construction] Systematic reconstruction of the knowledge system of Natural Civilization: what constitutes genuine knowledge (three conditions: observable, falsifiable, transmissible); the institutional design of the Natural Civilization university; the personality model of the Natural Civilization thinker; and 'Students of the Dao' as the civilizational alternative to two thousand years of 'Disciples of the Sage.' . (shrink)

Michel Serres’s philosophy of entropy takes what he famously calls the ‘Northwest Passage’ between the sciences and the humanities. By contextualizing his approach to entropy and affirming the role of a philosophy of difference, this paper explores Serres’s approach by means of ‘entropic differences’. It claims that entropy – or rather, entropies – provide Serres with a paradigmatic case for critical translations between different domains of knowledge. From his early Hermès series, through to The Birth of Physics (...) and later writings on social and ethical themes, he keeps thermodynamical and informational – or ‘hard’ and ‘soft’ – understandings of entropy apart, while simultaneously exploring their relation. By focusing on the systematic significance of Serres’s ‘entropic difference’, this paper shows how it unfolds not necessarily as an ontological difference but as an operative function between the history and philosophy of science, epistemology, and a theory of negentropic (inter)subjectivity. (shrink)

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this (...) paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)

This book is about an important issue which has arisen within two of the branches of physical science - namely thermodynamics and statistical mechanics - where the notion of entropy plays an essential role. A number of scientists and information theorists have maintained that entropy is a subjective concept and is a measure of human ignorance. Such a view, if it is valid, would create some profound philosophical problems and would tend to undermine the objectivity of the scientific (...) enterprise. Whilst the present volume is not a treatise on thermodynamics or statistical mechanics, all relevant steps in the building up of these disciplines are carefully scrutinised and it is concluded that the charge of subjectivity cannot be upheld. The widely adopted view that entropy is a measure of disorder, or of lack of information, is shown to be ambiguous, although it may be of use in certain contexts. (shrink)

Daniel R. Brooks and E. O. Wiley have proposed a theory of evolution in which fitness is merely a rate determining factor. Evolution is driven by non-equilibrium processes which increase the entropy and information content of species together. Evolution can occur without environmental selection, since increased complexity and organization result from the likely capture at the species level of random variations produced at the chemical level. Speciation can occur as the result of variation within the species which decreases the (...) probability of sharing genetic information. Critics of the Brooks-Wiley theory argue that they have abused terminology from information theory and t thermodynamics. In this paper I review the essentials of the theory, and give an account of hierarchical physical information systems within which the theory can be interpreted. I then show how the major conceptual objections can be answered. (shrink)

This article reconceptualizes entropy not as a metaphysical substance but as a structural constraint that shapes the formation, energetic cost, and durability of records. It links the coarse-grained—and typically irreversible—flow of time to questions of moral responsibility and divine justice. Drawing on the second law of thermodynamics, information theory, and contemporary cosmology, it advances an analogical and operational framework in which actions are accountable in an analogical sense insofar as they leave energetically costly traces that resist erasure. Within a (...) Qur’ānic metaphysical horizon, concepts such as kitāb (Book), ṣaḥīfa (Record), and tawba (Repentance) function as structural counterparts to informational inscription and revision, without reducing theological meaning to physical process. In contrast to Kantian ethics, which grounds moral law in rational autonomy, the Qurʾān situates responsibility within the irreversible structure of time. Understood in this way, entropy is not a threat to coherence but a condition for accountability. By placing the Qurʾānic vision in dialog with modern science and theology, the article contributes to broader discussions on justice, agency, and the metaphysics of time within the science–religion discourse. (shrink)

The paper tries to demonstrate that the process of the increase of entropy does not explain the asymmetry of time itself because it is unable to account for its fundamental asymmetries, that is, the asymmetry of traces (we have traces of the past and no traces of the future), the asymmetry of causation (we have an impact on future events with no possibility of having an impact on the past), and the asymmetry between the fixed past and the open (...) future, To this end, the approaches of Boltzmann, Reichenbach (and his followers), and Albert are analysed. It is argued that we should look for alternative approaches instead of this, namely we should consider a temporally asymmetrical physical theory or seek a source of the asymmetry of time in metaphysics. This second approach may even turn out to be complementary if only we accept that metaphysics can complement scientific research programmes. (shrink)

During language processing, context usually prompts predictions over multiple words, not a single word. We examined how the distribution of multiple plausible words following a context, that is, conditional entropy, influences lexical processing. Greater conditional entropy simultaneously corresponds to activation of more semantic features, which should facilitate processing, and activation of more lexical competitors, which should inhibit processing. Participants (N = 58) completed two experimental sessions 14–21 days apart. In session 1, they produced up to eight completions for (...) sentence fragments (N = 648), missing a final, target word (e.g., banana) along with probability values for each response. In session 2, they read the same sentences, including the target word, while their eye movements were tracked. We computed conditional entropy at the trial level (i.e., for each participant, for each sentence). To tease apart the semantic feature activation and lexical competition components of conditional entropy, we calculated total semantic overlap; the sum of semantic similarity values between target words and the responses produced during sentence completion (e.g., mango, orange, coconut, etc.). The remainder of conditional entropy would then capture lexical entropy corresponding to lexical competition. The results revealed that semantic overlap facilitated lexical processing, but lexical entropy inhibited it. A reanalysis of an independent self‐paced reading dataset (N participants = 111, N items = 647) revealed the same pattern. These results suggest that conditional entropy should be decomposed to semantic activation and lexical competition, corresponding to facilitation and inhibition during language processing, respectively. Implications for predictive processing views of language processing and large language models are discussed. (shrink)

Narrative Entropy (Sn) is a proposed quantitative descriptor within the Bulut Doctrine, intended to capture the rate at which a narrative text imposes processing load on a reader. To date the construct has been defined theoretically but not operationalized against real texts. This report documents the first such operationalization (the v2.0 pilot): two narrative scenes — the opening restaurant scene of Quentin Tarantino's Reservoir Dogs screenplay and the opening interior-monologue block of Raymond Carver's short story Cathedral — were coded (...) manually by a single rater and scored with the candidate formula Sn = If × Cb × t. -/- The result was contrary to intuitive expectation. The single-voice monologue block (Sn = 30.0) scored higher than the nine-character rapid-dialogue scene (Sn = 18.8). We treat this divergence not as a result to be explained away but as the central finding of the pilot, and we deliberately refuse post-hoc adjustment of the formula. We present three competing interpretations of the divergence formula incompleteness, genuine high-load prose, and measurement error — and we specify, in advance of data collection, the design that would discriminate among them. This document functions simultaneously as a pilot report (n = 2) and as a pre-registration of the next-stage protocol. It explicitly does not claim that Sn has been validated. -/- Keywords: narrative entropy, operationalization, pilot study, pre-registration, falsifiability, Bulut Doctrine, computational narratology, processing load. (shrink)

This paper analyzes the phenomenon of “intelligence divorced from wisdom” in modern high-entropy civilization from the perspective of scientific philosophical reflection. It argues that the true threat to civilization is not ignorance but highly intelligent individuals lacking wisdom and their cumulative systemic effects. In high-entropy civilizations, competition over technology, institutions, capital, and discourse rewards intelligence rather than wisdom, driving structural fragility, institutional hollowing, and systemic collapse. Through analysis of contemporary social phenomena, historical low-entropy experiments, and behavioral modeling (...) in the film Don’t Look Up, this study elucidates the operational logic of high-entropy civilization, the destructive effects of elite calculation, and the marginalization of wisdom in modern society. The research suggests that civilization can only reduce entropy and achieve sustainable development when intelligence is constrained by wisdom and aligned with natural laws. (shrink)

The language of entropy is examined for consistency with its mathematics and physics, and for its efficacy as a guide to what entropy means. Do common descriptors such as disorder, missing information, and multiplicity help or hinder understanding? Can the language of entropy be helpful in cases where entropy is not well defined? We argue in favor of the descriptor spreading, which entails space, time, and energy in a fundamental way. This includes spreading of energy spatially (...) during processes and temporal spreading over accessible microstates states in thermodynamic equilibrium. Various examples illustrate the value of the spreading metaphor. To provide further support for this metaphor’s utility, it is shown how a set of reasonable spreading properties can be used to derive the entropy function. A main conclusion is that it is appropriate to view entropy’s symbol S as shorthand for spreading. (shrink)

Markov models of evolution describe changes in the probability distribution of the trait values a population might exhibit. In consequence, they also describe how entropy and conditional entropy values evolve, and how the mutual information that characterizes the relation between an earlier and a later moment in a lineage’s history depends on how much time separates them. These models therefore provide an interesting perspective on questions that usually are considered in the foundations of physics—when and why does (...) class='Hi'>entropy increase and at what rates do changes in entropy take place? They also throw light on an important epistemological question: are there limits on what your observations of the present can tell you about the evolutionary past? (shrink)

This chapter explains the most important notions of entropy and clarifies their interrelations. It furthermore explores what notions of probabilities are at work when entropy is defined in terms of probability. Entropies from thermodynamics, information theory, statistical mechanics, dynamical systems theory, and fractal geometry are surveyed. Notions of entropy from statistical mechanics such as varieties of the Boltzmann and Gibbs entropies can be traced back to information-theoretic entropy. As the chapter points out, an analytic connection between (...) fine-grained Boltzmann entropy and thermodynamic entropy can be established for ideal gases. No easy results about probabilities follow, since several interpretations are compatible with each definition of entropy. (shrink)

We develop a theory of neural organization in which percepts are modeled as probabilistic structures on directed acyclic graphs of time-stamped subthreshold oscillatory states, and affective valence is defined by entropy dynamics on these structures. Each graph is assigned two pattern functors: a bound functor, whose elements are Bayesian networks compatible with the graph's causal organization, and an unbound functor, whose elements are arbitrary distributions on the corresponding vertex-state spaces. These functors are organized in a set-valued presheaf topos over (...) the category of directed acyclic graphs with ancestral inclusions, so that restriction corresponds to marginalization. Within this setting, percept-types are subfunctors, percepts are compatible families of local distributions, and the entropic valence determines a time-dependent Grothendieck topology governing which local patterns count as admissible for perceptual integration. The resulting internal intuitionistic logic provides a formal language for describing local endorsement, obstruction, and amalgamation of perceptual structure. We argue that this framework gives a principled account of how perceptual coherence and affective valence may jointly arise from mesoscopic cortical field dynamics. (shrink)

For the first time Entropy has been completely revised and updated to include a new subtitle which reflects the expanded focus on the greenhouse effect--the largest crisis ever to face mankind.

One of the consequences of the derivation of single-system entropy in the previous chapter was an assignment, to every state X∈Ξ[M]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\pmb {X}}\in \varXi [M]$$\end{document} of the system Σ[M]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varSigma [M]$$\end{document} a number SΣ(+)(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_\varSigma ^{(+)}({\pmb {X}})$$\end{document} or SΣ(-)(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_\varSigma ^{(-)}({\pmb {X}})$$\end{document}, according to whether the system is (...) i-simple or d-simple; this being the value of the single-system entropy at X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\pmb {X}}$$\end{document}. (shrink)

It is shown that entropy increase in thermodynamic systems can plausibly be accounted for by the random action of vacuum radiation. A recent calculation by Rueda using stochastic electrodynamics (SED) shows that vacuum radiation causes a particle to undergo a rapid Brownian motion about its average dynamical trajectory. It is shown that the magnitude of spatial drift calculated by Rueda can also be predicted by assuming that the average magnitudes of random shifts in position and momentum of a particle (...) correspond to the lower limits of the uncertainty relation. The latter analysis yields a plausible expression for the shift in momentum caused by vacuum radiation. It is shown that when the latter shift in momentum is magnified in particle interactions, the fractional change in each momentum component is on the order of unity within a few collision times, for gases and (plausibly) for denser systems over a very broad range of physical conditions. So any system of particles in this broad range of conditions would move to maximum entropy, subject to its thermodynamic constraints, within a few collision times. It is shown that the spatial drift caused by vacuum radiation, as predicted by the above SED calculation, can be macroscopic in some circumstances, and an experimental test of this effect is proposed. Consistency of the above results with quantum mechanics is discussed, and it is shown that the diffusion constant associated with the above Brownian drift is the same as that used in stochastic interpretations of the Schrödinger equation. (shrink)

Although the laws of thermodynamics are well established for black hole horizons, much less has been said in the literature to support the extension of these laws to more general settings such as an asymptotic de Sitter horizon or a Rindler horizon (the event horizon of an asymptotic uniformly accelerated observer). In the present paper we review the results that have been previously established and argue that the laws of black hole thermodynamics, as well as their underlying statistical mechanical content, (...) extend quite generally to what we call here “causal horizons.” The root of this generalization is the local notion of horizon entropy density. (shrink)

Both a method of therapy and an exploration of psychic reality, free association is a fundamental element of psychoanalytical practices that refers to the way a patient is asked to describe what comes spontaneously to mind in the therapeutic setting. This paper examines the role of free association from the point of view of psychoanalysis and neuroscience in order to improve our understanding of therapeutic effects induced by psychoanalytic therapies and psychoanalysis. In this regard, we first propose a global overview (...) of the historical origins of the concept of free association in psychoanalysis and examine how Freud established its principles. Then, from Freud’s distinction between primary and secondary processes, we proceed to compare the psychoanalytic model with research originating from cognitive psychology and neuroscience. The notions of entropy and free energy appear particularly relevant at the intersection of these different domains. Finally, we propose the notion of symbolizing transmodality to describe certain specificities of symbolization processes within free association and we summarize the main functions of free association in psychoanalytic practices. (shrink)

Entropy and information are both emerging as currencies of interdisciplinary dialogue, most recently in evolutionary theory. If this dialogue is to be fruitful, there must be general agreement about the meaning of these terms. That this is not presently the case owes principally to the supposition of many information theorists that information theory has succeeded in generalizing the entropy concept. The present paper will consider the merits of the generalization thesis, and make some suggestions for restricting both (...) class='Hi'>entropy and information to specific arenas of discourse. (shrink)

In theories of gravity with a positive cosmological constant, we consider product solutions with flux, of the form (A)dS p ×S q. Most solutions are shown to be perturbatively unstable, including all uncharged dS p ×S q spacetimes. For dimensions greater than four, the stable class includes universes whose entropy exceeds that of de Sitter space, in violation of the conjectured “N-bound.” Hence, if quantum gravity theories with finite-dimensional Hilbert space exist, the specification of a positive cosmological constant will (...) not suffice to characterize the class of spacetimes they describe. (shrink)

This essay is, primarily, a discussion of four results about the principle of maximizing entropy (MAXENT) and its connections with Bayesian theory. Result 1 provides a restricted equivalence between the two: where the Bayesian model for MAXENT inference uses an "a priori" probability that is uniform, and where all MAXENT constraints are limited to 0-1 expectations for simple indicator-variables. The other three results report on an inability to extend the equivalence beyond these specialized constraints. Result 2 established a sensitivity (...) of MAXENT inference to the choice of the algebra of possibilities even though all empirical constraints imposed on the MAXENT solution are satisfied in each measure space considered. The resulting MAXENT distribution is not invariant over the choice of measure space. Thus, old and familiar problems with the Laplacian principle of Insufficient Reason also plague MAXENT theory. Result 3 builds upon the findings of Friedman and Shimony (1971; 1973) and demonstrates the absence of an exchangeable, Bayesian model for predictive MAXENT distributions when the MAXENT constraints are interpreted according to Jaynes's (1978) prescription for his (1963) Brandeis Dice problem. Lastly, Result 4 generalizes the Friedman and Shimony objection to cross-entropy (Kullback-information) shifts subject to a constraint of a new odds-ratio for two disjoint events. (shrink)

Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set environment.

A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the axioms. First the Boltzmann–Planck formula is derived. Building on this formula, using the Law of Large Numbers—a basic theorem of probability theory—the von Neumann formula is deduced. Axioms used in older theories on the foundations are now derived facts.

The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow due to an expansion of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon (...) class='Hi'>entropy due to expansion is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the “force” accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum. (shrink)

I assess the thesis that counterfactual asymmetries are explained by an asymmetry of the global entropy at the temporal boundaries of the universe, by developing a method of evaluating counterfactuals that includes, as a background assumption, the low entropy of the early universe. The resulting theory attempts to vindicate the common practice of holding the past mostly fixed under counterfactual supposition while at the same time allowing the counterfactual's antecedent to obtain by a natural physical development. Although the (...) theory has some success in evaluating a wide variety of ordinary counterfactuals, it fails as an explanation of counterfactual asymmetry. (shrink)

I discuss the statistical mechanics of gravitating systems and in particular its cosmological implications, and argue that many conventional views on this subject in the foundations of statistical mechanics embody significant confusion; I attempt to provide a clearer and more accurate account. In particular, I observe that (i) the role of gravity in entropy calculations must be distinguished from the entropy of gravity, that (ii) although gravitational collapse is entropy-increasing, this is not usually because the collapsing matter (...) itself increases in entropy, and that (iii) the Second Law of thermodynamics does not owe its validity to the statistical mechanics of gravitational collapse. (shrink)

This essay is an attempt to reconcile the disturbing contradiction between the striving for order in nature and in man and the principle of entropy implicit in the second law of thermodynamics - between the tendency toward greater organization and the general trend of the material universe toward death and disorder.

The Anthropocene crisis is frequently described as the rarefaction of resources or resources per capita. However, both energy and minerals correspond to fundamentally conserved quantities from the perspective of physics. A specific concept is required to understand the rarefaction of available resources. This concept, entropy, pertains to energy and matter configurations and not just to their sheer amount. However, the physics concept of entropy is insufficient to understand biological and social organizations. Biological phenomena display both historicity and systemic (...) properties. A biological organization, the ability of a specific living being to last over time, results from history, expresses itself by systemic properties, and may require generating novelties The concept of anti-entropy stems from the combination of these features. We propose that Anthropocene changes disrupt biological organizations by randomizing them, that is, decreasing anti-entropy. Moreover, second-order disruptions correspond to the decline of the ability to produce functional novelties, that is, to produce anti-entropy. (shrink)

The notion of conditional entropy is extended to noncomposite systems. The \-deformed entropic inequalities, which usually are associated with correlations of the subsystem degrees of freedom in bipartite systems, are found for the noncomposite systems. New entropic inequalities for quantum tomograms of qudit states including the single qudit states are obtained. The Araki–Lieb inequality is found for systems without subsystems.

The present paper is a survey of the economics of survival, a branch of ecological economics that stresses the preservation of the opportunities of future generations over an extended time horizon. It outlines the main analytical foundation of the branch – in which the concept of entropy is a major building block –, and its analysis of the interaction between the economic system and the environment. Regarding its outlook of the future, we see that the founders of the branch (...) were mainly concerned with the consequences of a serious depletion of natural resources – particularly the energetic capital of the earth. More recently, however, emphasis is being placed on problems that stem from the fragility of the global ecosystem in face of the disturbances caused by the entropic acceleration imposed by mankind. It is feared that the ongoing expansion of the scale of the economy may bring about irreversible damages to vital environmental functions, such as protection against undesirable consequences of solar radiation, maintenance of temperature within a range that will support life, and preservation of ecosystem resiliency. (shrink)

We review some notions for general quantum entropies. The entropy of the compound systems is discussed and a numerical computation of the quantum dynamical systems is carried for the noisy optical channel.

This paper challenges the frequent demonisation of entropy in discourses which attempt to draw a “naturalised” axiology from thermodynamics, information theory, and related sciences. Such discourses include Wiener’s cybernetics, Stiegler’s negathropology, and Floridi’s information ethics, in each of which entropy designates the evil which must be fought in the name of life, information, or some other notion of “the good.” The perspective the paper develops is Nietzschean. Nietzsche himself rejected the consequences of the Second Law, but I wish (...) to argue that it is possible to affirm entropy, for Nietzschean reasons. First, the paper argues that the reason Nietzsche rejected the Second Law is that it provides consolation for the pessimist (an argument made by von Hartmann). Eternal return should be affirmed because it is the more difficult position, and so provides the ultimate existential test. However, metaphysical and existential reasons must give way to the more recent scientific evidence, especially the dating of the universe, which undermines Nietzsche’s argument against heat death. While this is alone sufficient reason to affirm entropy, the position is supported by two further classes of reasons. First, the oppositions which whave supported the traditional ascription of values to negentropy and entropy can be challenged; and 2) entropy can be seen as consonant with the characteristics of existence which Nietzsche sought to affirm, especially becoming. (shrink)

Disagreements over the meaning of the thermodynamic entropy and how it should be defined in statistical mechanics have endured for well over a century. In an earlier paper, I showed that there were at least nine essential properties of entropy that are still under dispute among experts. In this paper, I examine the consequences of differing definitions of the thermodynamic entropy of macroscopic systems.Two proposed definitions of entropy in classical statistical mechanics are (1) defining entropy (...) on the basis of probability theory (first suggested by Boltzmann in 1877), and (2) the traditional textbook definition in terms of a volume in phase space (also attributed to Boltzmann). The present paper demonstrates the consequences of each of these proposed definitions of entropy and argues in favor of a definition based on probabilities. (shrink)

ABSTRACT This paper argues that striving is a cardinal virtue in sport and life. It is an overlooked virtue that is an important component of human happiness and a source of a sense of dignity. The human psychological capacity for striving emerged as a trait for addressing the entropic features of our existence, but it can be engaged and used for other purposes. Sport is one such example. Sport appears exceptional in being designed specifically to test and display our capacities (...) to strive. Although striving is connected to pursuit of excellence in sport, it supports a more democratic conception of the value of sport than achievement-oriented perfectionist accounts. (shrink)

Two open questions of inductive reasoning are solved: (1) does the principle of maximum entropy (pme) give a solution to the obverse Majerník problem; and (2) is Wagner correct when he claims that Jeffrey’s updating principle (jup) contradicts pme? Majerník shows that pme provides unique and plausible marginal probabilities, given conditional probabilities. The obverse problem posed here is whether pme also provides such conditional probabilities, given certain marginal probabilities. The theorem developed to solve the obverse Majerník problem demonstrates that (...) in the special case introduced by Wagner pme does not contradict jup, but elegantly generalizes it and offers a more integrated approach to probability updating. (shrink)

Neural complexity and brain entropy have gained greater interest in recent years. The dynamics of neural signals and their relations with information processing continue to be investigated through different measures in a variety of noteworthy studies. The BEN of spontaneous neural activity decreases during states of reduced consciousness. This evidence has been showed in primary consciousness states, such as psychedelic states, under the name of “the entropic brain hypothesis.” In this manuscript we propose an extension of this hypothesis to (...) physiological and pathological aging. We review this particular facet of the complexity of the brain, mentioning studies that have investigated BEN in primary consciousness states, and extending this view to the field of neuroaging with a focus on resting-state functional Magnetic Resonance Imaging. We first introduce historic and conceptual ideas about entropy and neural complexity, treating the mindbrain as a complex nonlinear dynamic adaptive system, in light of the free energy principle. Then, we review the studies in this field, analyzing the idea that the aim of the neurocognitive system is to maintain a dynamic state of balance between order and chaos, both in terms of dynamics of neural signals and functional connectivity. In our exploration we will review studies both on acute psychedelic states and more chronic psychotic states and traits, such as those in schizophrenia, in order to show the increase of entropy in those states. Then we extend our exploration to physiological and pathological aging, where BEN is reduced. Finally, we propose an interpretation of these results, defining a general trend of BEN in primary states and cognitive aging. (shrink)

A probability distribution can be given to the set of isomorphism classes of models with universe {1, ..., n} of a sentence in first-order logic. We study the entropy of this distribution and derive a result from the 0–1 law for first-order sentences.

Entropy bounds have played an important role in the development of holography as an approach to quantum gravity, so in this article we seek to gain a better understanding of the covariant entropy bound. We observe that there is a possible way of thinking about the covariant entropy bound which would suggest that it encodes an epistemic limitation rather than an objective count of the true number of degrees of freedom on a light-sheet; thus we distinguish between (...) ontological and epistemic interpretations of the covariant bound. We consider the consequences that these interpretations might have for physics and we discuss what each approach has to say about gravitational phenomena. Our aim is not to advocate for either the ontological or epistemic approach in particular, but rather to articulate both possibilities clearly and explore some arguments for and against them. (shrink)

We investigate uncertain reasoning with quantified sentences of the predicate calculus treated as the limiting case of maximum entropy inference applied to finite domains.

This paper, based on the Lao–Yang Genesis Cosmology, argues that the rise and fall of civilization is determined not merely by institutional design or technological progress, but by the structural–entropy dynamics rooted in the cosmic hierarchy. Through systems philosophy and historical case analysis, the study elaborates the constraints of the Dao, the law of entropy, and the principles of natural civilization. It examines the structural characteristics of high-entropy civilizations, contrasts artificial and natural civilizations, reviews historical low-entropy (...) experiments such as the early American Republic, and analyzes the contemporary manifestation of global high-entropy civilization. The study concludes that civilization cannot be “saved” but must be constrained and guided in alignment with universal laws—this is the only rational strategy in a high-entropy world. -/- . (shrink)

Are principles of information processing necessary to demonstrate the consistency of statistical mechanics? Does the physical implementation of a computational operation have a fundamental thermodynamic cost, purely by virtue of its logical properties? These two questions lie at the centre of a large body of literature concerned with the Szilard engine (a variant of the Maxwell's demon thought experiment), Landauer's principle (supposed to embody the fundamental principle of the thermodynamics of computation) and possible connections between the two. A variety of (...) attempts to answer these questions have illustrated many open questions in the foundations of statistical mechanics. (shrink)