chemicalPotentialDefinition
plain-language theorem explainer
Chemical potential is introduced as the partial derivative of Helmholtz free energy with respect to particle number at fixed temperature and volume, equal to the energy cost of adding one particle. Recognition Science workers extending thermodynamics to J-cost gradients cite it as the base case for particle flow and ledger occupation. The entry is supplied by direct string assignment matching the classical expression.
Claim. The chemical potential is defined by $μ = (∂F/∂N)_{T,V}$, the energy required to add one particle at constant temperature $T$ and volume $V$.
background
Module THERMO-007 sets chemical potential as the energy cost to add one particle, the driver of flow from high to low values, and the quantity appearing in Fermi-Dirac and Bose-Einstein distributions. Recognition Science equates it to the J-cost gradient with respect to particle number so that particles move to minimize total J-cost and μ fixes ledger occupation. The definition draws on imported constants including G, RS-native units U, the J-cost functional equation, and the inflaton potential V to prepare gradient calculations.
proof idea
Direct definition that binds the string literal containing the partial-derivative expression to the identifier.
why it matters
The definition opens the chemical-potential development inside the Recognition Science thermodynamics layer and supplies the J-cost interpretation required by the module target. It supports later sibling declarations on ideal-gas μ, Fermi energy, Bose condensation, and reaction equilibrium. It anchors the link between classical thermodynamics and the recognition composition law without invoking the forcing chain or phi-ladder.
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