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Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities

Thermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR quantifies the minimal energetic cost of achieving a certain precision in determining a nonequilibrium c...

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Autores principales: Reiche, Daniel, Hsiang, Jen-Tsung, Hu, Bei-Lok
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9394344/
https://www.ncbi.nlm.nih.gov/pubmed/35892996
http://dx.doi.org/10.3390/e24081016
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author Reiche, Daniel
Hsiang, Jen-Tsung
Hu, Bei-Lok
author_facet Reiche, Daniel
Hsiang, Jen-Tsung
Hu, Bei-Lok
author_sort Reiche, Daniel
collection PubMed
description Thermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR quantifies the minimal energetic cost of achieving a certain precision in determining a nonequilibrium current. In this initial stage of our research program, our goal is to provide the quantum theoretical basis of TURs using microphysics models of linear open quantum systems where it is possible to obtain exact solutions. In paper [Dong et al., Entropy 2022, 24, 870], we show how TURs are rooted in the quantum uncertainty principles and the fluctuation–dissipation inequalities (FDI) under fully nonequilibrium conditions. In this paper, we shift our attention from the quantum basis to the thermal manifests. Using a microscopic model for the bath’s spectral density in quantum Brownian motion studies, we formulate a “thermal” FDI in the quantum nonequilibrium dynamics which is valid at high temperatures. This brings the quantum TURs we derive here to the classical domain and can thus be compared with some popular forms of TURs. In the thermal-energy-dominated regimes, our FDIs provide better estimates on the uncertainty of thermodynamic quantities. Our treatment includes full back-action from the environment onto the system. As a concrete example of the generalized current, we examine the energy flux or power entering the Brownian particle and find an exact expression of the corresponding current–current correlations. In so doing, we show that the statistical properties of the bath and the causality of the system+bath interaction both enter into the TURs obeyed by the thermodynamic quantities.
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spelling pubmed-93943442022-08-23 Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities Reiche, Daniel Hsiang, Jen-Tsung Hu, Bei-Lok Entropy (Basel) Article Thermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR quantifies the minimal energetic cost of achieving a certain precision in determining a nonequilibrium current. In this initial stage of our research program, our goal is to provide the quantum theoretical basis of TURs using microphysics models of linear open quantum systems where it is possible to obtain exact solutions. In paper [Dong et al., Entropy 2022, 24, 870], we show how TURs are rooted in the quantum uncertainty principles and the fluctuation–dissipation inequalities (FDI) under fully nonequilibrium conditions. In this paper, we shift our attention from the quantum basis to the thermal manifests. Using a microscopic model for the bath’s spectral density in quantum Brownian motion studies, we formulate a “thermal” FDI in the quantum nonequilibrium dynamics which is valid at high temperatures. This brings the quantum TURs we derive here to the classical domain and can thus be compared with some popular forms of TURs. In the thermal-energy-dominated regimes, our FDIs provide better estimates on the uncertainty of thermodynamic quantities. Our treatment includes full back-action from the environment onto the system. As a concrete example of the generalized current, we examine the energy flux or power entering the Brownian particle and find an exact expression of the corresponding current–current correlations. In so doing, we show that the statistical properties of the bath and the causality of the system+bath interaction both enter into the TURs obeyed by the thermodynamic quantities. MDPI 2022-07-23 /pmc/articles/PMC9394344/ /pubmed/35892996 http://dx.doi.org/10.3390/e24081016 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Reiche, Daniel
Hsiang, Jen-Tsung
Hu, Bei-Lok
Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities
title Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities
title_full Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities
title_fullStr Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities
title_full_unstemmed Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities
title_short Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities
title_sort quantum thermodynamic uncertainty relations, generalized current fluctuations and nonequilibrium fluctuation–dissipation inequalities
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9394344/
https://www.ncbi.nlm.nih.gov/pubmed/35892996
http://dx.doi.org/10.3390/e24081016
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AT hubeilok quantumthermodynamicuncertaintyrelationsgeneralizedcurrentfluctuationsandnonequilibriumfluctuationdissipationinequalities