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arXiv · 1911.04306

Quantum work statistics close to equilibrium

Matteo Scandi·Harry J. D. Miller·Janet Anders·Marti Perarnau-Llobet
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Abstract

We study the statistics of work, dissipation, and entropy production of a quantum quasi-isothermal process, where the system remains close to the thermal equilibrium along the transformation. We derive a general analytic expression for the work distribution and the cumulant generating function. All work cumulants split into a classical (non-coherent) and quantum (coherent) term, implying that close to equilibrium there are two independent channels of dissipation at all levels of the statistics. For non-coherent or commuting protocols, only the first two cumulants survive, leading to a Gaussian distribution with its first two moments related through the classical fluctuation-dissipation relation. On the other hand, quantum coherence leads to positive skewness and excess kurtosis in the distribution, and we demonstrate that these non-Gaussian effects are a manifestation of asymmetry in relation to the resource theory of thermodynamics. Furthermore, we also show that the non-coherent and coherent contributions satisfy independently the Evans-Searles fluctuation theorem, which sets strong bounds on the statistics, with negative values of the dissipation being exponentially suppressed. Our findings are illustrated in a driven two-level system and an Ising chain, where quantum signatures of the work distribution in the macroscopic limit are discussed.

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Matteo Scandi, Harry J. D. Miller, Janet Anders, Marti Perarnau-Llobet. 2019-11-11. Quantum work statistics close to equilibrium. https://doi.org/10.1103/physrevresearch.2.023377

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