IndisputableMonolith.Physics.ThermalPhysicsFromRS
Module linking thermal physics to Recognition Science via the J-cost: thermal equilibrium is identified with vanishing cost J = 0. It introduces heat-transfer mechanisms, an equilibrium predicate, and a certificate bundle. Physicists tracing RS thermodynamics cite it for the equilibrium convention. Structure is definitional plus lightweight certificates, not a deep derivation.
claimThermal equilibrium is the condition $J = 0$ on the Recognition cost. The module packages heat-transfer mechanisms, a count of those mechanisms, the equilibrium predicate, and a thermal-physics certificate tying the RS cost to equilibrium thermodynamics.
background
Recognition Science measures mismatch by the cost $J$, uniquely fixed (T5) as $J(x) = (x + x^{-1})/2 - 1$. Vanishing cost means perfect match: no residual recognition defect. This module takes that identification as the definition of thermal equilibrium.
It sits in the Physics domain and imports the Cost module for $J$ and related structure. Sibling objects name heat-transfer mechanisms, count them, state the equilibrium predicate, and bundle a certificate (ThermalPhysicsCert / thermalPhysicsCert) that the RS cost picture is the right language for equilibrium thermodynamics.
proof idea
This is largely a definition and certificate module, not a deep proof development. Equilibrium is declared as $J = 0$. Heat-transfer mechanisms and their count are introduced as named structure; the certificate packages the claim that thermal physics is recovered from the RS cost. No multi-step forcing or algebraic reduction is required beyond the Cost import.
why it matters in Recognition Science
Gives the RS reading of thermal equilibrium: zero cost, not an independent thermodynamic postulate. That convention is the bridge from the J-uniqueness forcing step (T5) and the Recognition Composition Law into ordinary thermal language. Downstream physics pages that need equilibrium as a hypothesis can cite the certificate and the $J = 0$ predicate rather than re-deriving the identification. No parent theorems are listed yet (used_by is empty); the module is a leaf packaging layer for thermal claims.
scope and limits
- Does not derive the laws of thermodynamics from first RS principles.
- Does not prove uniqueness of heat-transfer mechanisms beyond a named count.
- Does not connect equilibrium to the eight-tick octave or D = 3.
- Does not compute transport coefficients or temperature scales from phi.
- Does not discharge open scaffolding elsewhere in the monolith.