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We introduce an example of thermodynamic uncertainty relation (TUR) for systems modeled by a one-dimensional generalised Langevin dynamics with memory, determining the motion of a micro-bead driven in a complex fluid. Contrary to TURs…

Statistical Mechanics · Physics 2020-11-06 Ivan Di Terlizzi , Marco Baiesi

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

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

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

Thermodynamic uncertainty relations (TURs) bound the dissipation in non-equilibrium systems from below by fluctuations of an observed current. Contrasting the elaborate techniques employed in existing proofs, we here prove TURs directly…

Statistical Mechanics · Physics 2023-02-27 Cai Dieball , Aljaž Godec

In systems far from equilibrium, the statistics of observables are connected to entropy production, leading to the Thermodynamic Uncertainty Relation (TUR). However, the derivation of TURs often involves constraining the parity of…

Statistical Mechanics · Physics 2023-05-17 Domingos S. P. Salazar

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

Nonequilibrium current fluctuations represent one of the central topics in nonequilibrium physics. The thermodynamic uncertainty relation (TUR) is widely acclaimed for rigorously establishing a lower bound on current fluctuations, expressed…

Statistical Mechanics · Physics 2025-12-09 Van Tuan Vo , Andreas Dechant , Keiji Saito

Thermodynamic uncertainty relations yield a lower bound on entropy production in terms of the mean and fluctuations of a current. We derive their general form for systems under arbitrary time-dependent driving from arbitrary initial states…

Statistical Mechanics · Physics 2021-01-12 Timur Koyuk , Udo Seifert

Thermodynamic uncertainty relations (TURs) are the inequalities which give lower bounds on the entropy production rate using only the mean and the variance of fluctuating currents. Since the TURs do not refer to the full details of the…

Statistical Mechanics · Physics 2020-06-25 Shun Otsubo , Sosuke Ito , Andreas Dechant , Takahiro Sagawa

The thermodynamic uncertainty relation (TUR) imposes a fundamental constraint between current fluctuations and entropy production, providing a refined formulation of the second law for micro- and nanoscale systems. Quantum violations of the…

Quantum Physics · Physics 2026-01-28 Yang Li , Fu-Lin Zhang

Recently, some general relations have been studied in nonequilibrium mesoscopic systems. In particular, the thermodynamic uncertainty relation (TUR) provides a universal internal relation among the cumulants of currents and the entropy…

Statistical Mechanics · Physics 2021-07-07 Takaaki Monnai

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

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

Fluctuations affect the functionality of nanodevices. Thermodynamic uncertainty relations (TURs), derived within the framework of stochastic thermodynamics, show that a minimal amount of dissipation is required to obtain a given relative…

Quantum Physics · Physics 2024-09-13 Luca Razzoli , Matteo Carrega , Fabio Cavaliere , Giuliano Benenti , Maura Sassetti

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

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

Clocks are inherently out-of-equilibrium because, due to friction, they constantly consume free energy to keep track of time. The Thermodynamic Uncertainty Relation (TUR) quantifies the trade-off between the precision of any…

Statistical Mechanics · Physics 2024-02-05 Ashwin Gopal , Massimiliano Esposito , Nahuel Freitas

A new Thermodynamic Uncertainty Relation (TUR) is derived for systems described by linearly coupled Langevin equations in the presence of non-linear frictional forces. In our scheme, the main variable represents the velocity of a particle,…

Statistical Mechanics · Physics 2024-05-09 A. Plati , A. Puglisi , A. Sarracino

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