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The precision and response of trajectory observables offer valuable insights into the behavior of nonequilibrium systems. For classical systems, trade-offs between these characteristics and thermodynamic costs, such as entropy production…

Quantum Physics · Physics 2025-03-10 Tan Van Vu

The thermodynamic uncertainty relation (TUR) describes a trade-off relation between nonequilibrium currents and entropy production and serves as a fundamental principle of nonequilibrium thermodynamics. However, currently known TURs…

Statistical Mechanics · Physics 2020-09-30 Kangqiao Liu , Zongping Gong , Masahito Ueda

Fluctuation theorems establish that thermodynamic processes at the microscale can occasionally result in negative entropy production. At the microscale, another distinct possibility becomes more likely: processes in which no entropy is…

Statistical Mechanics · Physics 2026-03-11 Abhaya S. Hegde , André M. Timpanaro , Gabriel T. Landi

The Thermodynamic Uncertainty Relation (TUR) is a lower bound for the variance of a current as a function of the average entropy production and average current. Depending on the assumptions, one obtains different versions of the TUR. For…

Statistical Mechanics · Physics 2023-01-04 Domingos S. P. Salazar

Understanding current fluctuations is of fundamental importance and paves the way for the development of practical applications. According to the thermodynamic and kinetic uncertainty relations, the precision of currents can be constrained…

Statistical Mechanics · Physics 2022-10-06 Van Tuan Vo , Tan Van Vu , Yoshihiko Hasegawa

Thermodynamic uncertainty relations (TURs) are a set of inequalities expressing a fundamental trade-off between precision and dissipation in non-equilibrium classical and quantum thermodynamic processes. TURs show that achieving low…

Quantum Physics · Physics 2025-03-07 Mario Motta , Antonio Mezzacapo , Giacomo Guarnieri

The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is…

Statistical Mechanics · Physics 2020-12-29 Van Tuan Vo , Tan Van Vu , Yoshihiko Hasegawa

From a recent geometric generalization of Thermodynamic Uncertainty Relations (TURs) we derive novel upper bounds on the nonlinear response of an observable of an arbitrary system undergoing a change of probabilistic state. Various…

Statistical Mechanics · Physics 2022-03-09 Gianmaria Falasco , Massimiliano Esposito , Jean-Charles Delvenne

For fluctuating currents in non-equilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We show…

Statistical Mechanics · Physics 2017-07-12 Patrick Pietzonka , Felix Ritort , Udo Seifert

The thermodynamic uncertainty relation expresses a universal trade-off between precision and entropy production, which applies in its original formulation to current observables in steady-state systems. We generalize this relation to…

Statistical Mechanics · Physics 2018-12-06 Timur Koyuk , Udo Seifert , Patrick Pietzonka

The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of…

Statistical Mechanics · Physics 2019-06-11 Y. Mishin

In classical Markov jump processes, current fluctuations can only be reduced at the cost of increased dissipation. To explore how quantum effects influence this trade-off, we analyze the uncertainty of steady-state currents in Markovian…

Statistical Mechanics · Physics 2021-07-09 Paul Menczel , Eetu Loisa , Kay Brandner , Christian Flindt

The thermodynamic uncertainty relations (TURs) provide lower bounds on the entropy production (EP) of a system in terms of the statistical precision of an arbitrary current in that system. All conventional TURs derived so far have concerned…

Statistical Mechanics · Physics 2021-03-19 Gülce Kardeş , David H. Wolpert

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

For a generic class of machines with broken time-reversal symmetry we show that in the linear response regime the relative fluctuation of the sum of output currents for time-forward and time-reversed processes is always lower bounded by the…

Statistical Mechanics · Physics 2021-10-12 Sushant Saryal , Sandipan Mohanta , Bijay Kumar Agarwalla

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…

Statistical Mechanics · Physics 2022-08-02 Hang Dong , Daniel Reiche , Jen-Tsung Hsiang , Bei-Lok Hu

We derive a thermodynamic uncertainty relation (TUR) for first-passage times (FPTs) on continuous time Markov chains. The TUR utilizes the entropy production coming from bidirectional transitions, and the net flux coming from unidirectional…

Statistical Mechanics · Physics 2021-08-11 Arnab Pal , Shlomi Reuveni , Saar Rahav

A trade-off between the precision of an arbitrary current and the dissipation, known as the thermodynamic uncertainty relation, has been investigated for various Markovian systems. Here, we study the thermodynamic uncertainty relation for…

Statistical Mechanics · Physics 2019-09-23 Tan Van Vu , Yoshihiko Hasegawa

In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the non-equilibrium…

Statistical Mechanics · Physics 2021-08-17 David Hartich , Aljaz Godec

Thermodynamic uncertainty relations (TURs) express a fundamental tradeoff between the precision (inverse scaled variance) of any thermodynamic current by functionals of the average entropy production. Relying on purely variational…

Statistical Mechanics · Physics 2022-11-28 Kyle J. Ray , Alexander B. Boyd , Giacomo Guarnieri , James P. Crutchfield