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arXiv · 1810.09999

Heat conservation and fluctuations between quantum reservoirs in the Two-Time Measurement picture

Tristan Benoist·Annalisa Panati·Yan Pautrat
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Abstract

This work concerns the statistics of the Two-Time Measurement definition of heat variation in each reservoir of a thermodynamic quantum system. We study the cumulant generating function of the heat flows in the thermodynamic and large-time limits. It is well-known that, if the system is time-reversal invariant, this cumulant generating function satisfies the celebrated Evans--Searles symmetry. We show in addition that, under appropriate ultraviolet regularity assumptions on the local interaction between the reservoirs, it satisfies a translation-invariance property, as proposed in [Andrieux et al. New J. Phys. 2009]. We particularly fix some proofs of the latter article where the ultraviolet condition was not mentioned. We detail how these two symmetries lead respectively to fluctuation relations and a statistical refinement of heat conservation for isolated thermodynamic quantum systems. As in [Andrieux \emph{et al.} New J. Phys. 2009], we recover the Fluctuation-Dissipation Theorem in the linear response theory, short of Green--Kubo relations. We illustrate the general theory on a number of canonical models.

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Tristan Benoist, Annalisa Panati, Yan Pautrat. 2018-10-23. Heat conservation and fluctuations between quantum reservoirs in the Two-Time Measurement picture. https://arxiv.org/abs/1810.09999

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