2011/08/19 by Hao Ge, Ge, Hao, Woo Hyun Kim +4
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Biology Tumor Growth #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1108.4055
4 pages; no figure This paper has been withdrawn by the authors due to a crucial error in the master-equation part
openalex publication_date 2011/08/19 · arxiv created 2011/08/31 · arxiv updated 2011/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Master equation with microscopic reversibility (qij≠ 0 iff qji≠ 0) has a \em thermodynamic superstructure in terms of two state functions S, entropy, and F, free energy: It is discovered recently that entropy production rate ep=-dF/dt+Qhk with both -dF/dt=fd, Qhk ≥ 0. The free energy dissipation fd≥ 0 reflects irreversibility in spontaneous self-organization; house-keeping heat Qhk≥ 0 reveals broken time-symmetry in open system driven away from equilibrium. In a Riemannian geometric space, the master equation is a geodesic flow when Qhk=0; here we show that the ep decomposition is orthogonal: ep, fd, Qhk forms a pythagorean triples. Gradient flow means \em maximum dissipation principle outside Onsager's regime. The presence of Qhk makses gradient flow no longer generally true. Thermodynamics of stochastic physics requires a new geometric perspective.