IndisputableMonolith.Foundation.ThermodynamicLawsFromJCost
Derives the zeroth law and related thermodynamic laws from the J-cost function within Recognition Science. Equilibrium corresponds to J(r) = 0, which is equivalent to the ratio r equaling 1. The module builds these results on imports from the Constants and Cost modules to formalize entropy and other laws.
claimZeroth law: equilibrium holds if and only if $J(r) = 0$ if and only if $r = 1$. The module collects related derivations for entropy and the third law in RS-native units.
background
The module operates in the Foundation domain of Recognition Science and imports the fundamental RS time quantum with doc comment stating it equals 1 tick. It draws on the Cost module for the J-cost function that measures deviation from equilibrium. The supplied doc comment tightens the setting by equating equilibrium to vanishing J-cost at unit ratio, providing the bridge from the functional equation to thermodynamic statements.
proof idea
This is a definition module, no proofs. It organizes a collection of declarations that derive individual thermodynamic laws by applying properties of the J-cost imported from upstream modules.
why it matters in Recognition Science
This module feeds the broader Recognition Science framework by supplying thermodynamic interpretations of the J-cost that support derivations of physical laws. It contributes to the connection between cost functions and classical thermodynamics, aligning with the overall goal of deriving physics from the single functional equation.