2014/04/30 by Sergio Davis, Diego González
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Binary entropy function #Classical mechanics #Entropy (arrow of time) #Entropy maximization #Fisher information #H-theorem #Langevin equation #Mathematical optimization #Mathematics #Maximization #Maximum entropy thermodynamics #Nonlinear system #Path integral formulation #Phase space #Physics #Principle of maximum entropy #Quantum mechanics #Second law of thermodynamics #Statistical Mechanics and Entropy #Statistical physics #cond-mat.stat-mech #physics.data-an #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1751-8113/48/42/425003
published as J. Phys. A: Math. Theor. 48, 425003 (2015)
arxiv created 2015/09/07 · openalex publication_date 2015/09/22 · arxiv updated 2016/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker–Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker–Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the second law of thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the second law is a fundamental property of plausible inference.