Finite-bath corrections to the second law of thermodynamics

Physical Review. E
Jonathan G RichensLluis Masanes

Abstract

The second law of thermodynamics states that a system in contact with a heat bath can undergo a transformation if and only if its free energy decreases. However, the "if" part of this statement is only true when the effective heat bath is infinite. In this article we remove this idealization and derive corrections to the second law in the case where the bath has a finite size, or equivalently finite heat capacity. This can also be translated to processes lasting a finite time, and we show that thermodynamical reversibility is lost in this regime. We do so in full generality, without assuming any particular model for the bath; the only parameters defining the bath are its temperature and heat capacity. We find connections with second order Shannon information theory, in particular, in the case of Landauer erasure. We also consider the case of nonfluctuating work and derive finite-bath corrections to the min and max free energies employed in single-shot thermodynamics.

References

Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Michele CampisiPeter Hänggi
Dec 12, 2012·Physical Review Letters·O AbahE Lutz
Jun 27, 2013·Nature Communications·Michał Horodecki, Jonathan Oppenheim
Jun 27, 2013·Nature Communications·Johan Aberg
Feb 4, 2014·Physical Review Letters·Fernando G S L BrandãoRobert W Spekkens
Jun 28, 2014·Nature Communications·Paul SkrzypczykSandu Popescu
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Bartłomiej Gardas, Sebastian Deffner
Nov 26, 2016·Nature Communications·Jonathan G Richens, Lluis Masanes
Mar 16, 2017·Nature Communications·Lluís Masanes, Jonathan Oppenheim
Jan 20, 2018·Physical Review. E·Hiroyasu Tajima, Masahito Hayashi

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Citations

Nov 9, 2019·Physical Review Letters·Fabien ClivazMarcus Huber
Sep 24, 2019·Reports on Progress in Physics·Matteo Lostaglio
Sep 11, 2019·Physical Review. E·M Hamed Mohammady, Alessandro Romito

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