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As a fundamental measure of stability in nonequilibrium thermodynamics, fluctuations provide critical insight into the performance and reliability of heat engines. In this work, we establish universal fluctuation-dissipation bounds that…

Statistical Mechanics · Physics 2026-01-13 Ousi Pan , Zhiqiang Fan , Shunjie Zhang , Jie Li , Jincan Chen , Shanhe Su

Thermodynamic Uncertainty Relations (TURs) set universal bounds linking current fluctuations to entropy production in nonequilibrium steady states. Their multidimensional generalization (MTUR) introduces matrix inequalities connecting…

Mesoscale and Nanoscale Physics · Physics 2026-05-07 Sergi Vidal , Alba Mayor-Fernandez , Rosa Lopez

Work is a process-based quantity, and its measurement typically requires interaction with a measuring device multiple times. While classical systems allow for non-invasive and accurate measurements, quantum systems present unique challenges…

Quantum Physics · Physics 2025-06-17 Giulia Rubino , Karen V. Hovhannisyan , Paul Skrzypczyk

Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behaviour and for its possible application in near-term quantum technologies. However, understanding these…

Statistical Mechanics · Physics 2020-10-07 Federico Carollo , Carlos Pérez-Espigares

We present a general quantum fluctuation theorem for the entropy production of an open quantum system coupled to multiple environments, not necessarily at equilibrium. Such a general theorem, when restricted to the weak-coupling and…

Quantum Physics · Physics 2022-06-29 Gabriele De Chiara , Alberto Imparato

When an isolated quantum system is driven out of equilibrium, expectation values of general observables start oscillating in time. This article reviews the general theory of such temporal fluctuations. We first survey some results on the…

Statistical Mechanics · Physics 2015-09-02 Lorenzo Campos Venuti , Paolo Zanardi

Fluctuations are intrinsic to microscopic systems and impose fundamental limits on nonequilibrium precision, as captured by the thermodynamic uncertainty relation (TUR), which links current fluctuations to entropy production. While feedback…

Quantum Physics · Physics 2026-02-27 Ryotaro Honma , Tan Van Vu

Thermodynamic (TUR) and kinetic (KUR) uncertainty relations are fundamental bounds constraining the fluctuations of current observables in classical, non-equilibrium systems. Several works have verified, however, violations of these…

We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…

Probability · Mathematics 2026-05-06 Solesne Bourguin , Konstantinos Spiliopoulos

A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time-fluctuations of an observable \mathcal{A} are typically exponentially small in the system size. We consider here…

Statistical Mechanics · Physics 2013-01-22 Lorenzo Campos Venuti , Paolo Zanardi

The transient quantum fluctuation theorems of Crooks and Jarzynski restrict and relate the statistics of work performed in forward and backward forcing protocols. So far these theorems have been obtained under the assumption that the work…

Statistical Mechanics · Physics 2014-02-07 B. Prasanna Venkatesh , Gentaro Watanabe , Peter Talkner

The uncertainty principle is fundamentally rooted in the algebraic asymmetry between observables. We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry, where incompatibility is quantified by an…

Quantum Physics · Physics 2026-02-10 Xingze Qiu

We uncover the quantum fluctuation-response inequality, which, in the most general setting, establishes a bound for the mean difference of an observable at two different quantum states, in terms of the quantum relative entropy. When the…

Quantum Physics · Physics 2022-03-22 Yan Wang

The thermodynamic uncertainty relation offers a universal energetic constraint on the relative magnitude of current fluctuations in nonequilibrium steady states. However, it has only been derived for long observation times. Here, we prove a…

Statistical Mechanics · Physics 2017-08-30 Jordan M. Horowitz , Todd R. Gingrich

Determining the work which is supplied to a system by an external agent, provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a problem for quantum systems, where the standard…

Statistical Mechanics · Physics 2014-05-15 Gentaro Watanabe , B. Prasanna Venkatesh , Peter Talkner

We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…

Quantum Physics · Physics 2016-01-18 Reinhard F. Werner

We develop a comprehensive framework for characterizing fluctuations in quantum transport and nonequilibrium thermodynamics using two complementary approaches: full counting statistics and first-passage times. Focusing on open quantum…

Statistical Mechanics · Physics 2026-01-12 Paul Menczel , Christian Flindt , Fredrik Brange , Franco Nori , Clemens Gneiting

The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…

Statistical Mechanics · Physics 2018-02-21 Matthias Uhl , Patrick Pietzonka , Udo Seifert

We derive a universal thermodynamic uncertainty relation for Fermionic coherent transport, which bounds the total rate of entropy production in terms of the mean and fluctuations of a single particle current. This bound holds for any…

Statistical Mechanics · Physics 2025-07-29 Kay Brandner , Keiji Saito

We derive fluctuation-response inequalities for Markov jump processes that link the fluctuations of general observables to the response to perturbations in the transition rates within a unified framework. These inequalities are derived…

Statistical Mechanics · Physics 2025-11-14 Euijoon Kwon , Hyun-Myung Chun , Hyunggyu Park , Jae Sung Lee