Fluctuation, Dissipation and the Arrow of Time
Abstract
:1. Introduction
- Equilibrium Principle
- An isolated, macroscopic system which is placed in an arbitrary initial state within a finite fixed volume will attain a unique state of equilibrium.
- Second Law (Clausius)
- For a non-quasi-static process occurring in a thermally isolated system, the entropy change between two equilibrium states is non-negative.
- Second Law (Kelvin)
- No work can be extracted from a closed equilibrium system during a cyclic variation of a parameter by an external source.
2. The Fluctuation Theorem
2.1. Autonomous Dynamics
2.2. Nonautonomous Dynamics
- Second Law (Fluctuation Theorem)
- Injecting some amount of energy into a thermally insulated system at equilibrium at temperature T by the cyclic variation of a parameter, is exponentially (i.e., by a factor ) more probable than withdrawing the same amount of energy from it by the reversed parameter variation.
3. Dissipation: Kubo’s Formula
4. Implications for the Arrow of Time Question
5. Remarks
Acknowledgments
References and Notes
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Campisi, M.; Hänggi, P. Fluctuation, Dissipation and the Arrow of Time. Entropy 2011, 13, 2024-2035. https://doi.org/10.3390/e13122024
Campisi M, Hänggi P. Fluctuation, Dissipation and the Arrow of Time. Entropy. 2011; 13(12):2024-2035. https://doi.org/10.3390/e13122024
Chicago/Turabian StyleCampisi, Michele, and Peter Hänggi. 2011. "Fluctuation, Dissipation and the Arrow of Time" Entropy 13, no. 12: 2024-2035. https://doi.org/10.3390/e13122024
APA StyleCampisi, M., & Hänggi, P. (2011). Fluctuation, Dissipation and the Arrow of Time. Entropy, 13(12), 2024-2035. https://doi.org/10.3390/e13122024