Time：14:00-15:30, Friday, November 21 2025
Venue：E4-233
Speaker：Hong Qian, Westlake University
Title：The Mathematical Physics of Neo-Gibbsian Statistical Theory
Abstract: Generalization through novel interpretations of the inner logic of the century-old Gibbs' statistical thermodynamics is presented: i) Identifying k_B→0 as classical energetics, one directly derives a pair of thermodynamic variational formulae 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) that minimizes E/T−F(T)/T and Eeq(T) that minimizes E−TS(E). ii) In contradistinction, taking derivative of the cumulant generating function 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 brand 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. This is a joint work with B. Miao and Y.-S. Wu.
