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Quasistatic response for nonequilibrium processes: evaluating the Berry potential and curvature.

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Title: Quasistatic response for nonequilibrium processes: evaluating the Berry potential and curvature.
Authors: Beyen, Aaron1 (AUTHOR), Khodabandehlou, Faezeh1 (AUTHOR), Maes, Christian1 (AUTHOR) christian.maes@kuleuven.be
Source: Journal of Physics A: Mathematical & Theoretical. 2026, Vol. 59 Issue 19, p1-20. 20p.
Subjects: Jump processes, Thermodynamics, Entropy, Non-equilibrium reactions, Aharonov-Bohm effect, Geometric quantum phases, Thermodynamic functions
Abstract: We investigate how introducing slow, time-dependent perturbations to a steady, nonequilibrium process alters the expected (excess) values of important observables, such as the dynamical activity and entropy flux. When we make a cyclic thermodynamic transformation, the excesses are described in terms of a (geometric) Berry phase with corresponding Berry potential and Berry curvature quantifying the response. Focussing on Markov jump processes, we show how a non-zero Berry curvature leads to a breakdown of the thermodynamic Maxwell relations and of the Clausius heat theorem. We also present a variant of the Aharonov–Bohm effect in which the parameters follow a curve with vanishing Berry curvature, but the system still experiences a nonzero Berry phase. Finally, we identify (sufficient) no-localization conditions in terms of mean first-passage times under which the corresponding Berry potentials and curvatures vanish at absolute zero, extending, for arbitrary driving, e.g. the case of vanishing heat capacity as for the Nernst postulate. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:We investigate how introducing slow, time-dependent perturbations to a steady, nonequilibrium process alters the expected (excess) values of important observables, such as the dynamical activity and entropy flux. When we make a cyclic thermodynamic transformation, the excesses are described in terms of a (geometric) Berry phase with corresponding Berry potential and Berry curvature quantifying the response. Focussing on Markov jump processes, we show how a non-zero Berry curvature leads to a breakdown of the thermodynamic Maxwell relations and of the Clausius heat theorem. We also present a variant of the Aharonov–Bohm effect in which the parameters follow a curve with vanishing Berry curvature, but the system still experiences a nonzero Berry phase. Finally, we identify (sufficient) no-localization conditions in terms of mean first-passage times under which the corresponding Berry potentials and curvatures vanish at absolute zero, extending, for arbitrary driving, e.g. the case of vanishing heat capacity as for the Nernst postulate. [ABSTRACT FROM AUTHOR]
ISSN:17518113
DOI:10.1088/1751-8121/ae6ade