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

Reiche, Daniel; Hsiang, Jen-Tsung; Hu, Bei-Lok

doi:10.48550/arxiv.2206.09849

Cited by 1 publication

(2 citation statements)

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“…Lastly, looking at the big picture, we comment on two aspects extending what we have done here: (1) TURs in terms of currents: Many thermodynamic uncertainty relations are expressed in terms of thermodynamic quantities such as energy flux and entropy production in multiple-bath scenarios. In our next paper on this topic [ 28 ], the centerpiece is indeed TURs expressed in terms of heat flux. There, we need to evaluate the fluctuations of generalized currents which involve 4-point functions of the fields, causal Wick’s theorem, etc.…”

Section: Discussionmentioning

confidence: 99%

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Quantum Thermodynamic Uncertainties in Nonequilibrium Systems from Robertson-Schrödinger Relations

Dong

Reiche

Hsiang

et al. 2022

Entropy

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Thermodynamic uncertainty principles make up one of the few rare anchors in the largely uncharted waters of nonequilibrium systems, the fluctuation theorems being the more familiar. In this work we aim to trace the uncertainties of thermodynamic quantities in nonequilibrium systems to their quantum origins, namely, to the quantum uncertainty principles. Our results enable us to make this categorical statement: For Gaussian systems, thermodynamic functions are functionals of the Robertson-Schrödinger uncertainty function, which is always non-negative for quantum systems, but not necessarily so for classical systems. Here, quantum refers to noncommutativity of the canonical operator pairs. From the nonequilibrium free energy, we succeeded in deriving several inequalities between certain thermodynamic quantities. They assume the same forms as those in conventional thermodynamics, but these are nonequilibrium in nature and they hold for all times and at strong coupling. In addition we show that a fluctuation-dissipation inequality exists at all times in the nonequilibrium dynamics of the system. For nonequilibrium systems which relax to an equilibrium state at late times, this fluctuation-dissipation inequality leads to the Robertson-Schrödinger uncertainty principle with the help of the Cauchy-Schwarz inequality. This work provides the microscopic quantum basis to certain important thermodynamic properties of macroscopic nonequilibrium systems.

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Section: Discussionmentioning

confidence: 99%

“…In future work [ 28 ], we shall formulate specific uncertainty relations for thermodynamic quantities based on the results of this paper. Using the methodology of NEq quantum dynamics, we thereby provide some notable formulations in the literature with the connection to their microscopic foundations.…”

Section: Introductionmentioning

confidence: 99%