2014/11/30 by Alberto Montefusco, Francesco Consonni, Francesco Leonardo Consonni +1 · 38 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Cosmology and Gravitation Theories #Degenerate energy levels #Dissipation #Dissipative system #Entropy (arrow of time) #Mathematics #Non-equilibrium thermodynamics #Physics #Quantum mechanics #Statistical Mechanics and Entropy #Statistical physics #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.91.042138
published in Physical Review E 91(4), 042138 (American Physical Society) · 22 pages, 3 figures, to appear in Phys.Rev.E
arxiv created 2015/04/13 · openalex publication_date 2015/04/28 · arxiv updated 2015/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
By reformulating the steepest-entropy-ascent (SEA) dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry, we compare it with the primitive formulation of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) model and discuss the main technical differences of the two approaches. In both dynamical models the description of dissipation is of the "entropy-gradient" type. SEA focuses only on the dissipative, i.e., entropy generating, component of the time evolution, chooses a sub-Riemannian metric tensor as dissipative structure, and uses the local entropy density field as potential. GENERIC emphasizes the coupling between the dissipative and nondissipative components of the time evolution, chooses two compatible degenerate structures (Poisson and degenerate co-Riemannian), and uses the global energy and entropy functionals as potentials. As an illustration, we rewrite the known GENERIC formulation of the Boltzmann equation in terms of the square root of the distribution function adopted by the SEA formulation. We then provide a formal proof that in more general frameworks, whenever all degeneracies in the GENERIC framework are related to conservation laws, the SEA and GENERIC models of the dissipative component of the dynamics are essentially interchangeable, provided of course they assume the same kinematics. As part of the discussion, we note that equipping the dissipative structure of GENERIC with the Leibniz identity makes it automatically SEA on metric leaves.