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On Entropy Production of Repeated Quantum Measurements II. Examples

Tristan Benoist, N. Cuneo, V. Jakšić +1 more

arXiv:2012.03885Journal of Statistical PhysicsFeb 22, 202120 citations

On entropy production of repeated quantum measurements II. Examples

Tristan Benoist, Noé Cuneo, Jakšić, Vojkan +1 more

We illustrate the mathematical theory of entropy production in repeated quantum measurement processes developed in a previous work by studying examples of quantum instruments displaying various interesting phenomena and singularities. We emphasize the role of the thermodynamic formalism, and give many examples of quantum instruments whose resulting probability measures on the space of infinite sequences of outcomes (shift space) do not have the (weak) Gibbs property. We also discuss physically relevant examples where the entropy production rate satisfies a large deviation principle but fails to obey the central limit theorem and the fluctuation-dissipation theorem. Throughout the analysis, we explore the connections with other, a priori unrelated topics like functions of Markov chains, hidden Markov models, matrix products and number theory.We illustrate the mathematical theory of entropy production in repeated quantum measurement processes developed in a previous work by studying examples of quantum instruments displaying various interesting phenomena and singularities. We emphasize the role of the thermodynamic formalism, and give many examples of quantum instruments whose resulting probability measures on the space of infinite sequences of outcomes (shift space) do not have the (weak) Gibbs property. We also discuss physically relevant examples where the entropy production rate satisfies a large deviation principle but fails to obey the central limit theorem and the fluctuation-dissipation theorem. Throughout the analysis, we explore the connections with other, a priori unrelated topics like functions of Markov chains, hidden Markov models, matrix products and number theory.

Feb 22, 202119 citations

Entropy production in the quantum measurement of continuous observables

Pierre Gaspard

Physics Letters ANov 19, 20126 citations

On entropy production of repeated quantum measurements III. Quantum detailed balance

Tristan Benoist, Noé Cuneo, Vojkan Jakšić +1 more

In light of the dynamical-systems approach to entropy production in repeated quantum measurements, proposed and illustrated in Commun. Math. Phys. 357, 77-123 (2018) [arXiv:1607.00162] and J. Stat. Phys. 182, 44 (2021) [arXiv:2012.03885], we characterize the KMS quantum detailed balance condition for quantum channels via time-reversal invariance and the vanishing of the entropy production for the associated informationally complete quantum instruments.

arXiv:2511.00910Nov 2, 20250 citations

Stochastic entropy production in scattering theory

Ludovico Tesser, Henning Kirchberg, Matteo Acciai +1 more

We formulate a stochastic description of entropy production in scattering theory for coherent transport. We distinguish between the information entropy change due to partial knowledge of the leads' state and the thermodynamic entropy change due to the equilibration of each lead with its bath. By employing a two-point measurement scheme, we access the stochastic entropy production at these different stages of the process, as well as the statistics of generic transport quantities. When restricted to particle or energy transport, our approach reproduces the Landauer-Büttiker formulas. The possibility to consider more general quantities such as the entropy currents and their fluctuations, provides a systematic connection between stochastic thermodynamics and coherent transport.We formulate a stochastic description of entropy production in scattering theory for coherent transport. We distinguish between the information entropy change due to partial knowledge of the leads' state and the thermodynamic entropy change due to the equilibration of each lead with its bath. By employing a two-point measurement scheme, we access the stochastic entropy production at these different stages of the process, as well as the statistics of generic transport quantities. When restricted to particle or energy transport, our approach reproduces the Landauer-Büttiker formulas. The possibility to consider more general quantities such as the entropy currents and their fluctuations, provides a systematic connection between stochastic thermodynamics and coherent transport.

cond-mat.mes-hallCross-listedarXiv:2604.10322Apr 14, 2026

Quantum entropy and quantum measurements

Göran Lindblad

Springer eBooksApr 7, 200834 citations

On Entropy Production of Repeated Quantum Measurements I. General Theory

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