Jarzynski Equality, Crooks Fluctuation Theorem and the Fluctuation Theorems of Heat for Arbitrary Initial States

Abstract

By taking full advantage of the dynamic property imposed by the detailed balance condition, we derive a new refined unified fluctuation theorem (FT) for general stochastic thermodynamic systems. This FT involves the joint probability distribution functions of the final phase space point and a thermodynamic variable. Jarzynski equality, Crooks fluctuation theorem, and the FTs of heat as well as the trajectory entropy production can be regarded as special cases of this refined unified FT, and all of them are generalized to arbitrary initial distributions. We also find that the refined unified FT can easily reproduce the FTs for processes with the feedback control, due to its unconventional structure that separates the thermodynamic variable from the choices of initial distributions. Our result is heuristic for further understanding of the relations and distinctions between all kinds of FTs, and might be valuable for studying thermodynamic processes with information exchange.

15 pages, 1 table

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• Quantum-Classical Correspondence Principle for Work Distributions in a Chaotic System
• Exploring quasiprobability approach to quantum work in the presence of initial coherence: Advantages of the Margenau-Hill distribution
• Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations
• The First Law of Quantum Field Thermodynamics
• Understanding quantum work in a quantum many-body system
• Information Fluctuation Theorem for an Open Quantum Bipartite System
• The Heat Distribution of the Underdamped Langevin Equation
• Stochastic thermodynamics with odd controlling parameters
• Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs
• Stochastic thermodynamics of nonharmonic oscillators in high vacuum
• Verifying detailed fluctuation relations for discrete feedback-controlled quantum dynamics
• Equilibrium sampling by re-weighting non-equilibrium simulation trajectories
• Jarzynski matrix equality: calculating free energy difference by non-equilibrium simulations with an arbitrary initial distribution
• Thermodynamics of memory erasure via a spin reservoir
• Modified Jarzynski equality in a microcanonical ensemble
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