Stochastic Dynamics, Large Deviations Principle, and Non-equilibrium Thermodynamics

Abstract

By examining the deterministic limit of a general $\epsilon$-dependent generator for Markovian dynamics, which includes the continuous Fokker-Planck equations and discrete chemical master equations as two special cases, the intrinsic connections among mesoscopic stochastic dynamics, deterministic ODEs or PDEs, large deviations rate function, and macroscopic thermodynamic potential are established. Our result not only solves the long-lasting question on the origin of entropy function in classical irreversible thermodynamics, but also reveals an emergent feature that arises automatically during the deterministic limit, through its large deviations rate function, with both time-reversible dynamics equipped with a Hamiltonian function and time-irreversible dynamics equipped with an entropy function.

29 pages, 2 figures

References in corpus (6)

• The large deviation approach to statistical mechanics
• Frenetic bounds on the entropy production
• Analytical Mechanics in Stochastic Dynamics: Most Probable Path, Large-Deviation Rate Function and Hamilton-Jacobi Equation
• Large deviation for diffusions and Hamilton--Jacobi equation in Hilbert spaces
• The Einstein relation for the KPZ equation
• The Statistical Foundation of Entropy in Extended Irreversible Thermodynamics

Cited by in corpus (4)

• Field theories and quantum methods for stochastic reaction-diffusion systems
• Geometric Thermodynamics of Strain-Induced Crystallization in Polymers
• Exact Results in Stochastic Processes with Division, Death, and Diffusion: Spatial Correlations, Marginal Entropy Production, and Macroscopic Currents
• Recent Advances in Conservation-Dissipation Formalism for Irreversible Processes