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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

Stability and efficiency are mutually exclusive in a thermodynamic process, e.g. in a thermal machine. Any effort to reduce the fluctuations of a certain output quantity is necessarily accompanied by an increase of entropy production,…

Mesoscale and Nanoscale Physics · Physics 2026-05-14 Franco Mayo , Nahual Sobrino , Rosario Fazio , Fabio Taddei , Michele Governale

The thermodynamic uncertainty relation (TUR) quantifies a relationship between current fluctuations and dissipation in out-of-equilibrium overdamped Langevin dynamics, making it a natural counterpart of the fluctuation-dissipation theorem…

Statistical Mechanics · Physics 2022-10-04 Rueih-Sheng Fu , Todd R. Gingrich

We examine the so-called thermodynamic uncertainty relation (TUR), a cost-precision trade-off relationship in transport systems. Based on the fluctuation symmetry, we derive a condition on the validity of the TUR for general nonequilibrium…

Mesoscale and Nanoscale Physics · Physics 2018-10-31 Bijay Kumar Agarwalla , Dvira Segal

General upper bounds on fluctuations of trajectory observables were recently obtained. It turned out that the size of fluctuations of dynamical observable is limited from below and from above. For the moment generating function of general…

Statistical Mechanics · Physics 2025-05-13 V. V. Ryazanov

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 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…

Statistical Mechanics · Physics 2022-07-26 Daniel Reiche , Jen-Tsung Hsiang , Bei-Lok Hu

Current is a characteristic feature of nonequilibrium systems. In stochastic systems, these currents exhibit fluctuations constrained by the rate of dissipation in accordance with the recently discovered thermodynamic uncertainty relation.…

Statistical Mechanics · Physics 2017-10-30 Todd R. Gingrich , Jordan M. Horowitz

We investigate the thermodynamic uncertainty relations (TURs) in steady-state transport for a multi-terminal system consisting of two conducting terminals and N-2 probe terminals, within the linear response regime under broken time-reversal…

Statistical Mechanics · Physics 2026-01-07 Yanchao Zhang , Xinzhi Liu , Xiaolong Lü , Shanhe Su

Thermodynamic Uncertainty Relations express a trade-off between precision, defined as the noise-to-signal ratio of a generic current, and the amount of associated entropy production. These results have deep consequences for autonomous heat…

We study the statistics of first passage times (FPTs) of trajectory observables in both classical and quantum Markov processes. We consider specifically the FPTs of counting observables, that is, the times to reach a certain threshold of a…

Statistical Mechanics · Physics 2024-05-17 George Bakewell-Smith , Federico Girotti , Mădălin Guţă , Juan P. Garrahan

The thermodynamic uncertainty relation (TUR) is a fundamental principle in non-equilibrium thermodynamics that relates entropy production to fluctuations in a system, establishing a trade-off between the precision of an observable and the…

Quantum Physics · Physics 2025-08-07 Arghya Maity , Ahana Ghoshal

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

Thermodynamic uncertainty relations (TURs) represent a benchmark result in nonequilibrium physics that allows to place fundamental lower bounds on the noise-to-signal ratio (precision) of currents in nanoscale devices. Originally formulated…

Quantum Physics · Physics 2025-01-24 Andre M. Timpanaro , Giacomo Guarnieri , Gabriel T. Landi

We discuss how to use correlations between different physical observables to improve recently obtained thermodynamics bounds, notably the fluctuation-response inequality (FRI) and the thermodynamic uncertainty relation (TUR). We show that…

Statistical Mechanics · Physics 2022-01-10 Andreas Dechant , Shin-ichi Sasa

Thermodynamic uncertainty relations have emerged as universal bounds on current fluctuations in non-equilibrium systems. Here we derive a new bound for a particular class of run-and-tumble type processes using the mathematical framework of…

Statistical Mechanics · Physics 2019-07-02 Mayank Shreshtha , Rosemary J. Harris

A universal large $\mathcal{N}$ theory of nonequilibrium fluctuations emerges in the limit of fast jump rates and large occupancies. We use this theory to derive a set of coarse grained thermodynamic uncertainty relations (TUR) -- one of…

Statistical Mechanics · Physics 2022-01-12 Ohad Shpielberg , Arnab Pal

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

Thermodynamic uncertainty relations (TURs) set fundamental bounds on the fluctuation and dissipation of stochastic systems. Here, we examine these bounds, in experiment and theory, by exploring the entire phase space of a cyclic information…

Statistical Mechanics · Physics 2020-09-23 Govind Paneru , Sandipan Dutta , Tsvi Tlusty , Hyuk Kyu Pak

Thermodynamic uncertainty relation (TUR) provides a stricter bound for entropy production (EP) than that of the thermodynamic second law. This stricter bound can be utilized to infer the EP and derive other trade-off relations. Though the…

Statistical Mechanics · Physics 2021-11-24 Jae Sung Lee , Jong-Min Park , Hyunggyu Park