2025/08/24 by Miao, Bing, Qian, Hong, Wu, Yong-Shi
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2508.17548
Generalization through novel interpretations of the inner logic of the century-old Gibbs' statistical thermodynamics is presented: i) Identifying kB→ 0 as classical energetics, one directly derives a pair of thermodynamic variational formulae F(T) = min_E≥ Emin\E-TS(E) \ and \ S(E) = minTgt;0\(E)/(T)-(F(T))/(T) \, that dictate all the more familiar 1/T=d S(E)/d E, E=d\F(T)/T\/d(1/T), and S(E)=-d F(T)/d T in equilibrium, which is maintained by a duality symmetry with one-to-one relation between Teq(E)=argminT\E/T-F(T)/T\ and Eeq(T)=argminE\E-TS(E)\. ii) In contradistinction, taking derivative of the statistical free energy w.r.t. T, a mesoscopic energetics with fluctuations emerges: This yields two information entropy functions which historically appeared 50 years postdate Gibbs' theory. iii) Combining the above pair of inequalities yields an irreversible thermodynamic potential ψ(T,E) ≡ \E-F(T)\/T-S(E)≥ 0 for nonequilibrium states. The second law of thermodynamics as a universal principle reflects ψ≥ 0 due to a disagreement between E and T as a dual pair. Our theory provides a new energetics of living cells which are nonequilibrium, complex entities under constant T, pressure p and chemical potential μ. ψ provides a ``distance'' between statistical data from a large ensemble of cells and a set of intrinsic energetic parameters that encode the information within.