Analysis of entropy production in finitely slow processes between nonequilibrium steady states

Abstract

We investigate entropy production in finitely slow transitions between nonequilibrium steady states in Markov jump processes using the improved adiabatic approximation method proposed by Takahashi, Fujii, Hino and Hayakawa [1]. This method provides systematic improvement of the adiabatic approximation on infinitely slow transitions from which we obtain nonadiabatic corrections and has a close relationship with the slow driving perturbation [2, 3]. We analyze two types of excess entropy production of Sagawa and Hayakawa [4] and Hatano and Sasa [5] as examples, and confirm that the leading adiabatic contribution reproduces the known results, and then obtain nonadiabatic corrections written in terms of thermodynamic metrics defined in protocol parameter spaces. We also numerically study the resulting excess entropy production in a two-state system.

arXiv comment14 pages, 4 figures. v2:a reference added, a footnote added

References in corpus (24)

• 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
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Steady State Thermodynamics of Langevin Systems
• Full Counting Statistics of Charge Transfer in Coulomb Blockade Systems
• Three detailed fluctuation theorems
• The Physical Origins of Entropy Production, Free Energy Dissipation and their Mathematical Representations
• Integral fluctuation theorem for the housekeeping heat
• Slow dynamics and thermodynamics of open quantum systems
• Steady State Thermodynamics for Heat Conduction -- Microscopic Derivation
• The unified geometric theory of mesoscopic stochastic pumps and reversible ratchets
• Geometrical Expression of Excess Entropy Production
• A nonequilibrium extension of the Clausius heat theorem
• Analysis of slow transitions between nonequilibrium steady states
• Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States
• Nonadiabatic Control of Geometric Pumping
• Geometric decomposition of entropy production into excess, housekeeping and coupling parts
• Approximate thermodynamic structure for driven lattice gases in contact
• Geometrical Formulation of Adiabatic Pumping as a Heat Engine
• Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems
• Full counting statistics and fluctuation-dissipation relation for periodically driven two-state systems
• Noncyclic and nonadiabatic geometric phase for counting statistics
• Asymptotic expansion of the solution of the master equation and its application to the speed limit