Local non-equilibrium thermodynamics

Abstract

Local Shannon entropy lies at the heart of modern thermodynamics, with much discussion of trajectory-dependent entropy production. When taken at both boundaries of a process in phase space, it reproduces the second law of thermodynamics over a finite time interval for small scale systems. However, given that entropy is an ensemble property, it has never been clear how one can assign such a quantity locally. Given such a fundamental omission in our knowledge, we construct a new ensemble composed of trajectories reaching an individual microstate, and show that locally defined entropy, information, and free energy are properties of the ensemble, or trajectory-independent true thermodynamic potentials. We find that the Boltzmann-Gibbs distribution and Landauer's principle can be generalized naturally as properties of the ensemble, and that trajectory-free state functions of the ensemble govern the exact mechanism of non-equilibrium relaxation.

12 pages, 7 figures, concisely rewritten from the previous version

References in corpus (22)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Fluctuation theorem for stochastic dynamics
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Path ensembles averages in systems driven far-from-equilibrium
• Steady State Thermodynamics of Langevin Systems
• Generalized Jarzynski Equality under Nonequilibrium Feedback Control
• Dissipation: The phase-space perspective
• Second law and Landauer principle far from equilibrium
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Fluctuation Theorem with Information Exchange: Role of Correlations in Stochastic Thermodynamics
• Universal features in the energetics of symmetry breaking
• Information-Theoretic Limits of Control
• Dissipation and lag in irreversible processes
• Experimental free energy measurements of kinetic molecular states using fluctuation theorems
• Memory erasure in small systems
• Fluctuation relations for a driven Brownian particle
• Detailed Jarzynski Equality applied on a Logically Irreversible Procedure
• Fluctuation relations: a pedagogical overview

Cited by in corpus (4)

• Hydrodynamic instabilities in miscible fluids
• Ultra-low effective interfacial tension between miscible molecular fluids
• Roles of Local Non-equilibrium Free Energy in the Description of Biomolecules
• Fluctuation Theorem of Information Exchange within an Ensemble of Paths Conditioned on Correlated-Microstates