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.