Neo-Gibbsian statistical energetics with applications to nonequilibrium cells

Generalization through novel interpretations of the inner logic of the century-old Gibbs' statistical thermodynamics is presented: 1) identifying k_B → 0 as classical energetics without fluctuations, one directly derives a pair of thermodynamic variational formulae F(T)=minE≥E_minE-TS(E)andS(E)=minT>0ET-F(T)T, 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 T^eq(E) = arg min_T{E/T - F(T)/T} and E^eq(T) = arg min_E{E - TS(E)}. 2) In contradistinction, taking the derivative of Gibbs' statistical free energy with respect to T, a mesoscopic energetics with fluctuations emerges: This yields two information entropy functions that historically appeared 50 years postdate Gibbs' theory. 3) 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 that 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.