Entropic Fluctuations in Statistical Mechanics II. Quantum Dynamical Systems - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Entropic Fluctuations in Statistical Mechanics II. Quantum Dynamical Systems

Résumé

The celebrated Evans-Searles, respectively Gallavotti-Cohen, fluctuation theorem concerns certain universal statistical features of the entropy production rate of a classical system in a transient, respectively steady, state. In this paper, we consider and compare several possible extensions of these fluctuation theorems to quantum systems. In addition to the direct two-time measurement approach whose discussion is based on [LMP 114:32 (2024)], we discuss a variant where measurements are performed indirectly on an auxiliary system called ancilla, and which allows to retrieve non-trivial statistical information using ancilla state tomography. We also show that modular theory provides a way to extend the classical notion of phase space contraction rate to the quantum domain, which leads to a third extension of the fluctuation theorems. We further discuss the quantum version of the principle of regular entropic fluctuations, introduced in the classical context in [Nonlinearity 24, 699 (2011)]. Finally, we relate the statistical properties of these various notions of entropy production to spectral resonances of quantum transfer operators. The obtained results shed a new light on the nature of entropic fluctuations in quantum statistical mechanics.
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Dates et versions

hal-04706797 , version 1 (23-09-2024)

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  • HAL Id : hal-04706797 , version 1

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Tristan Benoist, Laurent Bruneau, Vojkan Jakšić, A. Panati, Claude-Alain Pillet. Entropic Fluctuations in Statistical Mechanics II. Quantum Dynamical Systems. 2024. ⟨hal-04706797⟩
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