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module module moderate

IndisputableMonolith.Thermodynamics.HeatCapacity

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The HeatCapacity module encodes the classical equipartition theorem inside Recognition Science by defining energy and heat-capacity contributions from quadratic Hamiltonian terms. It supplies explicit constructions for monatomic and diatomic cases that tie mode counting to the eight-tick cycle. Researchers deriving ideal-gas thermodynamics from the discrete RS clock cite these definitions. The module contains only definitions and no theorems.

claimEach quadratic term in the Hamiltonian contributes energy $k_B T/2$. Total internal energy is $U = (f/2) k_B T$ where $f$ is the number of modes obtained from the eight-tick structure.

background

Recognition Science places thermodynamics on the discrete eight-tick cycle whose phases run through $0, π/4, …, 7π/4$. The module imports the RS time quantum $τ_0 = 1$ tick together with external calibration anchors and the eight-tick foundation. It introduces classicalEnergy as the $kT/2$ contribution per quadratic term and builds classicalHeatCapacity, monatomicCv, and diatomicCv from mode counts derived via modes_from_8_tick.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the classical baseline that later thermodynamic constructions in the Recognition framework rest upon. It directly implements the equipartition statement quoted in its own doc-comment and links that statement to the eight-tick octave (T7) before any phi-ladder or quantum extensions are introduced.

scope and limits

depends on (3)

Lean names referenced from this declaration's body.

declarations in this module (21)