Universal Ideal Behavior and Macroscopic Work Relation of Linear Irreversible Stochastic Thermodynamics

Abstract

We revisit the Ornstein-Uhlenbeck (OU) process as the fundamental mathematical description of linear irreversible phenomena, with fluctuations, near an equilibrium. By identifying the underlying circulating dynamics in a stationary process as the natural generalization of classical conservative mechanics, a bridge between a family of OU processes with equilibrium fluctuations and thermodynamics is established through the celebrated Helmholtz theorem. The Helmholtz theorem provides an emergent macroscopic "equation of state" of the entire system, which exhibits a universal ideal thermodynamic behavior. Fluctuating macroscopic quantities are studied from the stochastic thermodynamic point of view and a non-equilibrium work relation is obtained in the macroscopic picture, which may facilitate experimental study and application of the equalities due to Jarzynski, Crooks, and Hatano and Sasa.

References in corpus (13)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Work and information processing in a solvable model of Maxwell's demon
• Two-temperature Langevin dynamics in a parabolic potential
• Work fluctuations in a time-dependent harmonic potential: rigorous results and beyond the overdamped limit
• A framework towards understanding mesoscopic phenomena: Emergent unpredictability, symmetry breaking and dynamics across scales
• Irreversible Thermodynamics in Multiscale Stochastic Dynamical Systems
• The Zeroth Law of Thermodynamics and Volume-Preserving Conservative Dynamics with Equilibrium Stochastic Damping
• Thermodynamics of the General Diffusion Process: Equilibrium Supercurrent and Nonequilibrium Driven Circulation with Dissipation
• Work Relations Connecting Nonequilibrium Steady States Without Detailed Balance
• Of dice and men. Subjective priors, gauge invariance, and nonequilibrium thermodynamics
• Foundations of Stochastic Thermodynamics
• Maximum Entropy Principle, Equal Probability a Priori and Gibbs Paradox

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