Thermodynamics as Recursion Rate Redistribution

Statistical thermodynamics (Boltzmann, Gibbs) provides the quantitative foundation
for thermodynamics confirmed across all experimental scales. This paper does not
challenge those results; it develops the geometric substrate from which thermodynamic
behaviour emerges in the Cohesion Unified Field Theory, extending the account begun in
the Thermodynamics as the Unifying Substrate paper [2]. Thermodynamics arises from
recursion rate redistribution within the continuous recursion medium. Temperature
corresponds to local recursion rate variance; entropy to the number of accessible
recursion rate configurations; heat flow to pressure-driven recursion equalization; and
equilibrium to the uniformisation of structural time. The second law is structural
time monotonicity: structural time increases because pressure equalizes recursion rates.
The Helmholtz free energy analogue in this framework is the usable recursion capacity
FR = R − TR SR (where TR is recursion variance and SR is recursion configuration
count, both in recursion-rate units); recovering the standard Helmholtz formula requires
specifying the energy-recursion connection, which is an open problem. Black hole and
cosmological thermodynamics are special cases of the same recursion rate redistribution,
unified under a single geometric account within the Cohesion UFT framework.