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Stochastic entropy production: Fluctuation relation and irreversibility mitigation in non-unital quantum dynamics
Quantum Physics · Submitted 14 Oct 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In particular, we prove a fluctuation relation for the latter and we find a convenient way of expressing its average solely in terms of relative entropies.
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The abstract, sentence by sentence
In this work, we study the stochastic entropy production in open quantum systems whose time evolution is described by a class of non-unital quantum maps. In particular, as in [Phys. Rev. E 92, 032129 (2015)], we consider Kraus operators that can be related to a nonequilibrium potential. This class accounts for both thermalization and equilibration to a non-thermal state. Unlike unital quantum maps, non-unitality is responsible for an unbalance of the forward and backward dynamics of the open quantum system under scrutiny. Here, concentrating on observables that commute with the invariant state of the evolution, we show how the non-equilibrium potential enters the statistics of the stochastic entropy production. In particular, we prove a fluctuation relation for the latter and we find a convenient way of expressing its average solely in terms of relative entropies. Then, the theoretical results are applied to the thermalization of a qubit with non-Markovian transient, and the phenomenon of irreversibility mitigation, introduced in [Phys. Rev. Research 2, 033250 (2020)], is analyzed in this context.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this work, we study the stochastic entropy production in open quantum systems whose time evolution is described by a class of non-unital quantum maps. | contribution 0.97 | 0.82 | 0.04 | asserted 0.93 |
| s1 | In particular, as in [Phys. Rev. E 92, 032129 (2015)], we consider Kraus operators that can be related to a nonequilibrium potential. | method 0.68 | 0.22 | 0.03 | asserted 0.96 |
| s2 | This class accounts for both thermalization and equilibration to a non-thermal state. | background 0.61 | 0.18 | 0.04 | asserted 1.00 |
| s3 | Unlike unital quantum maps, non-unitality is responsible for an unbalance of the forward and backward dynamics of the open quantum system under scrutiny. | background 0.77 | 0.13 | 0.09 | asserted 1.00 |
| s4 | Here, concentrating on observables that commute with the invariant state of the evolution, we show how the non-equilibrium potential enters the statistics of the stochastic entropy production. | contribution 0.64 | 0.93 | 0.15 | asserted 1.00 |
| s5 | In particular, we prove a fluctuation relation for the latter and we find a convenient way of expressing its average solely in terms of relative entropies. | result 0.95 | 0.96 | 0.45 | asserted 1.00 |
| s6 | Then, the theoretical results are applied to the thermalization of a qubit with non-Markovian transient, and the phenomenon of irreversibility mitigation, introduced in [Phys. Rev. Research 2, 033250 (2020)], is analyzed in this context. | contribution 0.89 | 0.78 | 0.17 | asserted 0.99 |
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Original abstract
In this work, we study the stochastic entropy production in open quantum systems whose time evolution is described by a class of non-unital quantum maps. In particular, as in [Phys. Rev. E 92, 032129 (2015)], we consider Kraus operators that can be related to a nonequilibrium potential. This class accounts for both thermalization and equilibration to a non-thermal state. Unlike unital quantum maps, non-unitality is responsible for an unbalance of the forward and backward dynamics of the open quantum system under scrutiny. Here, concentrating on observables that commute with the invariant state of the evolution, we show how the non-equilibrium potential enters the statistics of the stochastic entropy production. In particular, we prove a fluctuation relation for the latter and we find a convenient way of expressing its average solely in terms of relative entropies. Then, the theoretical results are applied to the thermalization of a qubit with non-Markovian transient, and the phenomenon of irreversibility mitigation, introduced in [Phys. Rev. Research 2, 033250 (2020)], is analyzed in this context.
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How the literature uses it
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Papers citing it
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It should be noted that the relationship between entropy production in out-of-equilibrium systems and its coarse-grained counterpart has already been extensively studied [ref] .
Brownian particles in periodic potentials: coarse-graining versus fine structure · Different bin sizes · 0.98
What it cites · 1 sentence without a confident label
Uses the method or tool of 1 paper
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In this paper, we adopt the point of view of stochastic quantum thermodynamics, so that the entropy production is defined as a stochastic variable, whose probability distribution and statistical moments can be computed by resorting to the Tasaki-Crooks formalism [ref] .
Jarzynski Relations for Quantum Systems and Some Applications · Introduction · 0.98
Cites as background 1 paper
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The study of non-Markovian quantum dynamics became an active area of research in the last decade [ref] .
Dynamical maps beyond Markovian regime · Case-study: Qubit thermalization with non-Markovian transient · 1.00
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