Entropy as Wave: The Second Law as a Local Gradient of Periodic Constraint Structure

The second law of thermodynamics is confirmed in every experiment ever conducted, yet itsempirical basis spans less than 0.000002% of cosmic history. All extrapolation beyond thedirect observation window rests on retrodiction from present-day constraint patterns,mediated by the Past Hypothesis—an inference from the current entropy gradient, not anindependent observation. We show that this inference is formally underdetermined: amonotonic trajectory and the ascending phase of a periodic trajectory are observationallyindistinguishable within the available window. We survey five independent researchprograms—Penrose’s conformal cyclic cosmology, Barbour’s Janus Point, the Carroll-Chenand Boyle-Turok symmetric cosmologies, Price’s defense of time-symmetric boundaryconditions, and the Page curve in black hole physics—that have each demonstrated, throughdifferent methods and in response to different problems, that entropy increase is local,emergent, and bounded rather than global, fundamental, and monotonic. Their convergenceconstitutes the evidential basis for the wave hypothesis: that entropy increase is the ascendinglocal gradient of a larger periodic constraint structure. Observational data on cosmic entropyproduction—peaking at redshift z ≈ 2 and decelerating since—favor an asymmetricrelaxation-oscillation waveform over a simple sinusoid. We propose the van der Pol oscillatorin the strongly nonlinear regime as a formal candidate and show that Adlam’s framework oflaws as atemporal constraints provides the philosophical infrastructure for periodic entropy.The hypothesis generates testable predictions concerning entropy deceleration profiles,time-varying dark energy, and CMB signatures.