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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

The thermodynamic uncertainty relation (TUR) provides a universal entropic bound for the precision of the fluctuation of the charge transfer for example for a class of continuous time stochastic processes. However, its extension to general…

Statistical Mechanics · Physics 2022-04-20 Takaaki Monnai

Thermodynamic Uncertainty Relations (TURs) are relations that establish lower bounds for the relative fluctuations of thermodynamic quantities in terms of the statistics of the associated entropy production. In this work we derive a family…

Statistical Mechanics · Physics 2026-03-24 André M. Timpanaro

For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from…

Quantum Physics · Physics 2023-09-27 Domingos S. P. Salazar

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

Thermodynamic uncertainty relations (TURs) are general lower bounds on the size of fluctutations of dynamical observables. They have important consequences, one being that the precision of estimation of a current is limited by the amount of…

Statistical Mechanics · Physics 2022-10-12 George Bakewell-Smith , Federico Girotti , Mădălin Guţă , Juan P. Garrahan

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

In quantum thermodynamics, entropy production is usually defined in terms of the quantum relative entropy between two states. We derive a lower bound for the quantum entropy production in terms of the mean and variance of quantum…

Quantum Physics · Physics 2024-04-30 Domingos S. P. Salazar

Thermodynamic uncertainty relations (TURs) place strict bounds on the fluctuations of thermodynamic quantities in terms of the associated entropy production. In this work we identify the tightest (and saturable) matrix-valued TUR that can…

Quantum Physics · Physics 2019-10-07 André M. Timpanaro , Giacomo Guarnieri , John Goold , Gabriel T. Landi

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

We derive a universal thermodynamic uncertainty relation (TUR) that applies to an arbitrary observable in a general Markovian system. The generality of our result allows us to make two findings: (1) for an arbitrary out-of-equilibrium…

Statistical Mechanics · Physics 2022-06-07 Liu Ziyin , Masahito Ueda

We derive a thermodynamic uncertainty relation (TUR) for systems with unidirectional transitions. The uncertainty relation involves a mixture of thermodynamic and dynamic terms. Namely, the entropy production from bidirectional transitions,…

Statistical Mechanics · Physics 2021-03-30 Arnab Pal , Shlomi Reuveni , Saar Rahav

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

In nonequilibrium systems, the relative fluctuation of a current has a universal trade-off relation with the entropy production, called the thermodynamic uncertainty relation (TUR). For systems with broken time reversal symmetry, its…

Statistical Mechanics · Physics 2021-10-04 Jong-Min Park , Hyunggyu Park

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

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

We introduce a new technique to bound the fluctuations exhibited by a physical system, based on the Euclidean geometry of the space of observables. Through a simple unifying argument, we derive a sweeping generalization of so-called…

Statistical Mechanics · Physics 2020-06-24 Gianmaria Falasco , Massimiliano Esposito , Jean-Charles Delvenne

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) has been well studied for systems with few degrees of freedom. While, in principle, the TUR holds for more complex systems with many interacting degrees of freedom as well, little is known so far…

Statistical Mechanics · Physics 2022-11-22 Timur Koyuk , Udo Seifert
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