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Fluctuation relations and strong inequalities for thermally isolated systems

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  • Jarzynski, Christopher

Abstract

For processes during which a macroscopic system exchanges no heat with its surroundings, the second law of thermodynamics places two lower bounds on the amount of work performed on the system: a weak bound, expressed in terms of a fixed-temperature free energy difference, W≥ΔFT, and a strong bound, given by a fixed-entropy internal energy difference, W≥ΔES. It is known that statistical inequalities related to the weak bound can be obtained from the nonequilibrium work relation, 〈e−βW〉=e−βΔFT. Here we derive an integral fluctuation relation 〈e−βX〉=1 that is constructed specifically for adiabatic processes, and we use this result to obtain inequalities related to the strong bound, W≥ΔES. We provide both classical and quantum derivations of these results.

Suggested Citation

  • Jarzynski, Christopher, 2020. "Fluctuation relations and strong inequalities for thermally isolated systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 552(C).
    • Handle: RePEc:eee:phsmap:v:552:y:2020:i:c:s0378437119312075
    DOI: 10.1016/j.physa.2019.122077
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    References listed on IDEAS

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    1. Swendsen, Robert H. & Wang, Jian-Sheng, 2016. "Negative temperatures and the definition of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 24-34.
    2. Federico Cerisola & Yair Margalit & Shimon Machluf & Augusto J. Roncaglia & Juan Pablo Paz & Ron Folman, 2017. "Using a quantum work meter to test non-equilibrium fluctuation theorems," Nature Communications, Nature, vol. 8(1), pages 1-6, December.
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