The Tolman Entropy Problem Revisited: A Relational Invariant Approach to Cyclic Cosmology

The Tolman entropy problem has long been regarded as a decisive objection to cyclic cosmological models, based on the assumption that entropy necessarily accumulates from cycle tocycle. In this work, we argue that this conclusion relies on an implicit identification betweenentropy and inter-cycle memory. By disentangling local thermodynamic irreversibility fromglobal cosmological inheritance, we show that entropy need not be transmitted across cycles.We introduce the concept of a relational cycle invariant, which governs inter-cycle consistencywithout preserving microphysical state information. From this perspective, the Tolman entropyproblem is reformulated as an assumption about cosmological memory rather than a fundamental thermodynamic constraint. This shift provides a robust conceptual foundation for a newclass of cyclic models that remain consistent with thermodynamic irreversibility while avoidingcumulative inter-cycle degradation.