Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Thermodynamics
- 2 Statistical Mechanics
- 3 Hydrodynamics
- 4 Stochastic Processes
- 5 Fluctuation Relations for Energy and Particle Fluxes
- 6 Path Probabilities, Temporal Disorder, and Irreversibility
- 7 Driven Brownian Particles and Related Systems
- 8 Effusion Processes
- 9 Processes in Dilute and Rarefied Gases
- 10 Fluctuating Chemohydrodynamics
- 11 Reactions
- 12 Active Processes
- 13 Transport in Hamiltonian Dynamical Models
- 14 Quantum Statistical Mechanics
- 15 Transport in Open Quantum Systems
- Appendix A Complements on Thermodynamics
- Appendix B Complements on Dynamical Systems Theory
- Appendix C Complements on Statistical Mechanics
- Appendix D Complements on Hydrodynamics
- Appendix E Complements on Stochastic Processes
- Appendix F Complements on Fluctuation Relations
- References
- Index
5 - Fluctuation Relations for Energy and Particle Fluxes
Published online by Cambridge University Press: 14 July 2022
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Thermodynamics
- 2 Statistical Mechanics
- 3 Hydrodynamics
- 4 Stochastic Processes
- 5 Fluctuation Relations for Energy and Particle Fluxes
- 6 Path Probabilities, Temporal Disorder, and Irreversibility
- 7 Driven Brownian Particles and Related Systems
- 8 Effusion Processes
- 9 Processes in Dilute and Rarefied Gases
- 10 Fluctuating Chemohydrodynamics
- 11 Reactions
- 12 Active Processes
- 13 Transport in Hamiltonian Dynamical Models
- 14 Quantum Statistical Mechanics
- 15 Transport in Open Quantum Systems
- Appendix A Complements on Thermodynamics
- Appendix B Complements on Dynamical Systems Theory
- Appendix C Complements on Statistical Mechanics
- Appendix D Complements on Hydrodynamics
- Appendix E Complements on Stochastic Processes
- Appendix F Complements on Fluctuation Relations
- References
- Index
Summary
The fluctuations of energy and particle fluxes obey remarkable symmetries called fluctuation relations, which are valid arbitrarily far from equilibrium and find their origin in microreversibility. Yet they imply the nonnegativity of entropy production in accord with the second law of thermodynamics. They express the directionality of nonequilibrium processes, reducing at equilibrium to the conditions of detailed balance. The nonequilibrium work fluctuation relation and Jarzynski’s equality are presented in the absence and the presence of a magnetizing field and also for joint angular momentum transfer. Moreover, the multivariate fluctuation relation for all the fluxes across an open system in contact with several reservoirs is deduced from both the classical Hamiltonian microdynamics and the theory of stochastic processes. The multivariate fluctuation relation implies not only the fluctuation–dissipation theorem and the Onsager–Casimir reciprocal relations close to equilibrium but also their generalizations to the nonlinear response properties of relevance farther away from equilibrium.
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- The Statistical Mechanics of Irreversible Phenomena , pp. 202 - 256Publisher: Cambridge University PressPrint publication year: 2022