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For current fluctuations in non-equilibrium steady states of Markovian processes, we derive four different universal bounds valid beyond the Gaussian regime. Different variants of these bounds apply to either the entropy change or any…

Statistical Mechanics · Physics 2016-05-31 Patrick Pietzonka , Andre C. Barato , Udo Seifert

This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the…

Quantum Physics · Physics 2025-12-30 Sounak Bandyopadhyay , Arnab Ghosh

The thermodynamic uncertainty relation offers a universal energetic constraint on the relative magnitude of current fluctuations in nonequilibrium steady states. However, it has only been derived for long observation times. Here, we prove a…

Statistical Mechanics · Physics 2017-08-30 Jordan M. Horowitz , Todd R. Gingrich

The intuition that the precision of observables is constrained by thermodynamic costs has recently been formalized through thermodynamic and kinetic uncertainty relations. While such trade-offs have been extensively studied in Markovian…

Quantum Physics · Physics 2026-05-13 Tan Van Vu , Ryotaro Honma , Keiji Saito

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

Out-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of non-equilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are…

Statistical Mechanics · Physics 2023-01-19 Prajwal Padmanabha , Daniel Maria Busiello , Amos Maritan , Deepak Gupta

We extend a class of recently derived thermodynamic uncertainty relations to vector-valued observables. In contrast to the scalar-valued observables examined previously, this multidimensional thermodynamic uncertainty relation provides a…

Statistical Mechanics · Physics 2019-10-22 Andreas Dechant

The fluctuation theorem is the fundamental equality in nonequilibrium thermodynamics that is used to derive many important thermodynamic relations, such as the second law of thermodynamics and the Jarzynski equality. Recently, the…

Statistical Mechanics · Physics 2019-09-16 Yoshihiko Hasegawa , Tan Van Vu

Physical systems that power motion and create structure in a fixed amount of time dissipate energy and produce entropy. Whether living or synthetic, systems performing these dynamic functions must balance dissipation and speed. Here, we…

Statistical Mechanics · Physics 2020-12-18 Schuyler B. Nicholson , Luis Pedro Garcia-Pintos , Adolfo del Campo , Jason R. Green

We generalize the thermodynamic uncertainty relation, providing an entropic upper bound for average fluxes in time-continuous steady-state systems (Gingrich et al., Phys. Rev. Lett. 116, 120601 (2016)), to time-discrete Markov chains and to…

Statistical Mechanics · Physics 2017-10-11 Karel Proesmans , Christian Van den Broeck

The thermodynamic uncertainty relation, which establishes a universal trade-off between the relative fluctuation of arbitrary currents and the dissipation, has been found for various Markovian systems. However, this relation has not been…

Statistical Mechanics · Physics 2019-07-31 Tan Van Vu , Yoshihiko Hasegawa

We derive a quantum extension of the thermodynamic uncertainty relation where dynamical fluctuations are quantified by the Terletsky-Margenau-Hill quasiprobability, a quantum generalization of the classical joint probability. The obtained…

Quantum Physics · Physics 2026-03-31 Kohei Yoshimura , Ryusuke Hamazaki

Thermo-Kinetic relations bound thermodynamic quantities such as entropy production with statistics of dynamical observables. We introduce a Thermo-Kinetic Relation to bound the entropy production or the non-adiabatic (Hatano-Sasa, excess)…

Statistical Mechanics · Physics 2022-06-06 Jean-Charles Delvenne , Gianmaria Falasco

The thermodynamic behavior of Markovian open quantum systems can be described at the level of fluctuations by using continuous monitoring approaches. However, practical applications require assessing imperfect detection schemes, where the…

The exploration of far-from-equilibrium systems has been at the forefront of nonequilibrium thermodynamics, with a particular focus on understanding the fluctuations and response of thermodynamic systems to external perturbations. In this…

Statistical Mechanics · Physics 2025-02-13 Kangqiao Liu , Jie Gu

We analyze thermodynamic bounds on equilibrium fluctuations of an order parameter, which are analogous to relations, which have been derived recently in the context of non-equilibrium fluctuations of currents. We discuss the case of {\it…

Statistical Mechanics · Physics 2016-12-14 J. Guioth , D. Lacoste

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

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

Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…

Statistical Mechanics · Physics 2024-05-14 Gonzalo Manzano , Gülce Kardeş , Édgar Roldán , David 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