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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

Quantum conductors attached to metallic reservoirs have been demonstrated to overcome the thermodynamic uncertainty relation (TUR), a trade-off relation between the amount of dissipation and the absence of charge and heat current…

Mesoscale and Nanoscale Physics · Physics 2025-11-06 David Christian Ohnmacht , Juan Carlos Cuevas , Wolfgang Belzig , Rosa López , Jong Soo Lim , Kun Woo Kim

Recently, a thermodynamic uncertainty relation (TUR) has been formulated for classical Markovian systems demonstrating trade-off between precision (current fluctuation) and cost (dissipation). Systems that violate the TUR are interesting as…

Mesoscale and Nanoscale Physics · Physics 2019-07-03 Junjie Liu , Dvira Segal

We use the fundamental nonequilibrium steady-state fluctuation symmetry and derive a condition on the validity of the thermodynamic uncertainty relation (TUR) in thermal transport problems, classical or quantum alike. We test this condition…

Mesoscale and Nanoscale Physics · Physics 2019-10-09 Sushant Saryal , Hava Friedman , Dvira Segal , Bijay Kumar Agarwalla

The thermodynamic uncertainty relation (TUR) is expected to hold in nanoscale electronic conductors, when the electron transport process is quantum coherent and the transmission probability is constant (energy and voltage independent). We…

Mesoscale and Nanoscale Physics · Physics 2020-05-20 Hava Meira Friedman , Bijay Kumar Agarwalla , Ofir Shein-Lumbroso , Oren Tal , Dvira Segal

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

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

We investigate transient version of the recently discovered thermodynamic uncertainty relation (TUR) which provides a precision-cost trade-off relation for certain out-of-equilibrium thermodynamic observables in terms of net entropy…

Statistical Mechanics · Physics 2021-03-03 Sushant Saryal , Onkar Sadekar , Bijay Kumar Agarwalla

Thermodynamic uncertainty relations (TURs) bound the precision of currents by entropy production, but quantum transport of noncommuting (non-Abelian) charges challenges standard formulations because different charge components cannot be…

Quantum Physics · Physics 2026-01-01 Domingos S. P. Salazar

A cost-precision trade-off relationship, the so-called thermodynamic uncertainty relation (TUR), has been recently discovered in stochastic thermodynamics. It bounds certain thermodynamic observables in terms of the associated entropy…

Statistical Mechanics · Physics 2020-05-27 Soham Pal , Sushant Saryal , Dvira Segal , T. S. Mahesh , Bijay Kumar Agarwalla

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

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

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) 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

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

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

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) 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

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 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
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