Thermodynamics as Recursion Rate Redistribution

Statistical thermodynamics (Boltzmann, Gibbs) provides the quantitative foundationfor thermodynamics confirmed across all experimental scales. This paper does notchallenge those results; it develops the geometric substrate from which thermodynamicbehaviour emerges in the Cohesion Unified Field Theory, extending the account begun inthe Thermodynamics as the Unifying Substrate paper [2]. Thermodynamics arises fromrecursion rate redistribution within the continuous recursion medium. Temperaturecorresponds to local recursion rate variance; entropy to the number of accessiblerecursion rate configurations; heat flow to pressure-driven recursion equalization; andequilibrium to the uniformisation of structural time. The second law is structuraltime monotonicity: structural time increases because pressure equalizes recursion rates.The Helmholtz free energy analogue in this framework is the usable recursion capacityFR = R − TR SR (where TR is recursion variance and SR is recursion configurationcount, both in recursion-rate units); recovering the standard Helmholtz formula requiresspecifying the energy-recursion connection, which is an open problem. Black hole andcosmological thermodynamics are special cases of the same recursion rate redistribution,unified under a single geometric account within the Cohesion UFT framework.