Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production

Abstract

The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence of the positive invariant measure with density is established and a weak form of Foguel alternative proven. We show the equivalence among self-adjoint of the elliptic operator, time-reversibility, and zero entropy production rate of the stationary diffusion process. A thermodynamic theory for diffusion processes emerges.

23 pages

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• A Decomposition of Irreversible Diffusion Processes Without Detailed Balance
• Irreversible Thermodynamics in Multiscale Stochastic Dynamical Systems
• Characterising the nonequilibrium stationary states of Ornstein-Uhlenbeck processes
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• Thermodynamics of the General Diffusion Process: Equilibrium Supercurrent and Nonequilibrium Driven Circulation with Dissipation
• Gaussian noise and time-reversal symmetry in non-equilibrium Langevin models
• Stochastic Thermodynamics Across Scales: Emergent Inter-attractoral Discrete Markov Jump Process and Its Underlying Continuous Diffusion
• Irreversible Samplers from Jump and Continuous Markov Processes
• Temporal Behavior of the Conditional and Gibbs' Entropies
• Effects of Noise on Entropy Evolution
• The Measure-theoretic Identity Underlying Transient Fluctuation Theorems
• Kinematic Basis of Emergent Energetics of Complex Dynamics
• Fitness and entropy production in a cell population dynamics with epigenetic phenotype switching
• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Work
• Mesoscopic and Macroscopic Entropy Balance Equations in a Stochastic Dynamics and Its Deterministic Limit