Internal Energy, Fundamental Thermodynamic Relation, and Gibbs’ Ensemble Theory as Emergent Laws of Statistical Counting
Year: 2024
Type: article
Abstract: Statistical counting ad infinitum is the holographic observable to a statistical dynamics with finite states under independent and identically distributed N sampling. Entropy provides the infinitesimal probability for an observed empirical frequency ν^ with respect to a probability prior p, when ν^≠p as N→∞. Following Callen’s postulate and through Legendre–Fenchel transform, without help from mechanics, we show that an internal energy u emerges; it provides a linear representation of real-valued observables with full or partial information. Gibbs’ fundamental thermodynamic relation and theory of ensembles follow mathematically. u is to ν^ what chemical potential μ is to particle number N in Gibbs’ chemical thermodynamics, what β=T−1 is to internal energy U in classical thermodynamics, and what ω is to t in Fourier analysis.
Source: Entropy
DOI: 10.3390/e26121091
Author: Hong Qian
Institution: University of Washington
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4405374387