pith. sign in
def

summary

definition
show as:
module
IndisputableMonolith.Thermodynamics.HeatCapacity
domain
Thermodynamics
line
220 · github
papers citing
none yet

plain-language theorem explainer

The definition supplies a five-item list that condenses the Recognition Science account of heat capacity. A researcher deriving specific heats from mode counting would cite the list to recall equipartition, 8-tick structure, and the Debye and Dulong-Petit limits. The content is assembled by direct enumeration with no computation or lemma calls.

Claim. The summary is the list [``Equipartition: $kT/2$ per mode'', ``8-tick phases determine mode structure'', ``Quantum: modes freeze at low $T$'', ``Debye $T^3$ from 3D structure'', ``Dulong-Petit: $3R$ at high $T$'']

background

The module derives heat capacity formulas from 8-tick mode counting. Heat capacity at constant volume is the partial derivative of internal energy with respect to temperature; each quadratic mode receives $kT/2$ under equipartition. In Recognition Science the active modes are fixed by the phase patterns of the eight-tick octave.

proof idea

The definition directly constructs and returns the list of five strings. No lemmas or tactics are invoked; the body is a literal enumeration of the module's perspective statements.

why it matters

The list anchors the thermodynamics module by collecting the statements that follow from the eight-tick octave and three-dimensional structure. It prepares the ground for quantitative derivations of $C_V$ and $C_P$ via mode counting, consistent with T7 and T8 of the forcing chain. No downstream theorems reference it yet.

Switch to Lean above to see the machine-checked source, dependencies, and usage graph.