Fluctuation relations: a pedagogical overview
Abstract
The fluctuation relations have received considerable attention since their emergence and development in the 1990s. We present a summary of the main results and suggest ways to interpret this material. Starting with a consideration of the under-determined time evolution of a simple open system, formulated using continuous Markovian stochastic dy- namics, an expression for the entropy generated over a time interval is developed in terms of the probability of observing a trajectory associated with a prescribed driving protocol, and the probability of its time-reverse. This forms the basis for a general theoretical description of non-equilibrium thermodynamic pro- cesses. Having established a connection between entropy production and an inequivalence in probability for forward and time-reversed events, we proceed in the manner of Sekimoto and Seifert, in particular, to derive results in stochastic thermodynamics: a description of the evolution of a system between equilibrium states that ties in with well-established thermodynamic expectations. We derive fluctuation relations, state conditions for their validity, and illustrate their op- eration in some simple cases, thereby providing some introductory insight into the various celebrated symmetry relations that have emerged in this field.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2012
- DOI:
- 10.48550/arXiv.1201.6381
- arXiv:
- arXiv:1201.6381
- Bibcode:
- 2012arXiv1201.6381S
- Keywords:
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- Condensed Matter - Statistical Mechanics
- E-Print:
- Chapter contributed to R.Klages, W.Just, C.Jarzynski (Eds.), Nonequilibrium Statistical Physics of Small Systems: Fluctuation Relations and Beyond (Wiley-VCH, Weinheim, 2012