Local Detailed Balance : A Microscopic Derivation

Abstract

Thermal contact is the archetype of non-equilibrium processes driven by constant non-equilibrium constraints when the latter are enforced by reservoirs exchanging conserved microscopic quantities. At a mesoscopic scale only the energies of the macroscopic bodies are accessible together with the configurations of the contact system. We consider a class of models where the contact system, as well as macroscopic bodies, have a finite number of possible configurations. The global system with only discrete degrees of freedom has no microscopic Hamiltonian dynamics, but it is shown that, if the microscopic dynamics is assumed to be deterministic and ergodic and to conserve energy according to some specific pattern, and if the mesoscopic evolution of the global system is approximated by a Markov process as closely as possible, then the mesoscopic transition rates obey three constraints. In the limit where macroscopic bodies can be considered as reservoirs at thermodynamic equilibrium (but with different intensive parameters) the mesoscopic transition rates turn into transition rates for the contact system and the third constraint becomes local detailed balance ; the latter is generically expressed in terms of the microscopic exchange entropy variation, namely the opposite of the variation of the thermodynamic entropy of the reservoir involved in a given microscopic jump of the contact system configuration. For a finite-time evolution after contact has been switched on we derive a fluctuation relation for the joint probability of the heat amounts received from the various reservoirs. The generalization to systems exchanging energy, volume and matter with several reservoirs, with a possible conservative external force acting on the contact system, is given explicitly.

arXiv comment26 pages. arXiv admin note: substantial text overlap with arXiv:1302.4538

References in corpus (15)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Path ensembles averages in systems driven far-from-equilibrium
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Steady State Thermodynamics of Langevin Systems
• Stochastic thermodynamics: Principles and perspectives
• Three detailed fluctuation theorems
• Fluctuation theorems for stochastic dynamics
• Classical and Quantum Fluctuation Theorems for Heat Exchange
• Fluctuation theorem for currents and Schnakenberg network theory
• Cumulants and large deviations of the current through non-equilibrium steady states
• Entropy production for mechanically or chemically driven biomolecules
• Exact fluctuation theorem without ensemble quantities

Cited by in corpus (8)

• Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
• Macroscopic Stochastic Thermodynamics
• Local detailed balance across scales: from diffusions to jump processes and beyond
• Methods and Conversations in (Post)Modern Thermodynamics
• Reversal symmetries for cyclic paths away from thermodynamic equilibrium
• Entropy balance and Information processing in bipartite and non-bipartite composite systems
• Sterically Driven Current Reversal in a Model Molecular Motor
• Information ratchets exploiting spatially structured information reservoirs