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<p>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 Benoist et al. (Lett Math Phys 114:32, 2024. <a href="https://doi.org/10.1007/s11005-024-01777-0">https://doi.org/10.1007/s11005-024-01777-0</a>), 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 Jakšić et al. (Nonlinearity 24:699, 2011. <a href="https://doi.org/10.1088/0951-7715/24/3/003">https://doi.org/10.1088/0951-7715/24/3/003</a>). 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.</p>

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Entropic Fluctuations in Statistical Mechanics II. Quantum Dynamical Systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月1日

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  • T. Benoist,
  • L. Bruneau,
  • V. Jakšić,
  • A. Panati,
  • C.-A. Pillet

摘要

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 Benoist et al. (Lett Math Phys 114:32, 2024. https://doi.org/10.1007/s11005-024-01777-0), 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 Jakšić et al. (Nonlinearity 24:699, 2011. https://doi.org/10.1088/0951-7715/24/3/003). 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.