Fluctuation Relations: A Pedagogical Overview

By Richard E. Spinney, Ian J. Ford. 2012

52 citations recorded by the source corpus.

The uctuation relations have received considerable attention since their emergence and development in the 1990s. As an aid to newcomers to the eld, 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 dynamics, an expression for the entropy generated with time is proposed 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 more complete theoretical description of non-equilibrium thermodynamic processes. 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 uctuation relations, state conditions for their validity, and illustrate their operation in some simple cases, thereby providing some introductory insight into the various celebrated symmetry relations that have emerged in this eld.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics, Evaluation & Benchmarks

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Citations in the corpus

Deep Unsupervised Learning using Nonequilibrium Thermodynamics (2015, background): “In thermodynamics the schedule taken when moving between equilibrium distributions determines how much free energy is lost [38, 17].”
Near-optimal protocols in complex nonequilibrium transformations (2016, background): “For a single trajectory x(t) the dissipation ω can be cast in terms of an imbalance between forward and reversed dynamics [10] with,”