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On Entropy Production of Repeated Quantum Measurements I. General Theory

Tristan Benoist, V. Jakšić, Yan Pautrat +1 more

arXiv:1607.00162Communications in Mathematical PhysicsJul 14, 201748 citations

Entropy production in the quantum measurement of continuous observables

Pierre Gaspard

Physics Letters ANov 19, 20126 citations

Quantum measurement and entropy production

Paolo Grigolini A, Marco G. Pala, Luigi Palatella

arXiv:cond-mat/0007323Physics Letters AJun 1, 200113 citations

Quantum entropy production as a measure of irreversibility

I. Callens, Wojciech De Roeck, T Jacobs +2 more

arXiv:cond-mat/0211252Physica D Nonlinear PhenomenaNov 20, 200334 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

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

On Entropy Production of Repeated Quantum Measurements II. Examples

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