Biophys J. 2026 Jan 30:S0006-3495(26)00057-3. doi: 10.1016/j.bpj.2026.01.042. Online ahead of print.
ABSTRACT
Generalization through novel interpretations of the inner logic of the century-old Gibbs’ statistical thermodynamics is presented: i) Identifying kB → 0 as classical energetics without fluctuations, one directly derives a pair of thermodynamic variational formulae [Formula: see text] ,that dictate all the more familiar 1/T = dS(E)/dE, E = d{F(T)/T}/d(1/T), and S(E) = -dF(T)/dT in equilibrium, which is maintained by a duality symmetry with one-to-one relation between Teq(E) = arg minT{E/T – F(T)/T} and Eeq(T) = arg minE{E – TS(E)}. ii) In contradistinction, taking derivative of Gibbs’ 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 potentials μ1, μ2, etc., with sustained μ1 – μ2 ≠ 0. 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.
PMID:41620826 | DOI:10.1016/j.bpj.2026.01.042
