Abstract

Existing cyclic cosmologies face an unanswered question: how are successive cosmological cycles thermodynamically related? If each cycle begins from entirely new initial conditions, cosmic history is repeatedly erased. If every feature carries unchanged into the next cycle, each universe is an exact repetition of its predecessor. Neither is physically satisfactory, and the problem is now observationally urgent. Recent results from the Dark Energy Spectroscopic Instrument suggest that dark energy is weakening over cosmic time rather than remaining constant (Abdul Karim et al., 2025; Luu et al., 2025). A weakening dark energy has a decay curve—a rate of change—and the question of what drives that curve, and what happens when it reaches the Friedmann turning point, is no longer purely speculative. If collapse within cosmological timescales is physically plausible, the question of what follows, and whether it is continuous with what preceded it, deserves a framework. This paper proposes a framework connecting four otherwise independent theoretical programs—dynamical dark energy, Loop Quantum Cosmology, thermodynamic irreversibility, and cyclic cosmological models—through a single directional principle: irreversible differentiation. The framework treats differentiation as the primitive process from which cosmic directionality emerges. Because differentiations are irreversible, they generate persistent consequences—residue, defined here as the accumulated constraint geometry generated by irreversible differentiation, the persistent deformation of the probability distribution over available future states. Entropy production is one measurable expression of this directionality at local scales; dark energy evolution is proposed as its parallel expression at cosmological scales. The two are not causally related—neither drives the other—but both may be parallel manifestations of the same underlying directional process, tracking each other across cosmic time because both are expressions of the universe moving from its founding differentiation toward increasing uniformity. The framework does not require every one of these proposals to be correct. It requires only that if they are each partially correct, they fit together in the way described here. The paper develops this framework across seven sections, formulates a phenomenological mathematical model consistent with it, identifies four observational predictions by which its central claims may be confirmed or falsified, and derives in Appendix B the framework’s most distinctive structural consequence: that thermodynamic inheritance across LQC bounces produces a cosmological sequence that is neither symmetric nor infinite, but directional and terminable by a precisely specifiable condition.