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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

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

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) impose a universal trade-off between current precision and entropy production in autonomous steady states, constraining in particular the power, efficiency, and constancy of heat engines. We…

Statistical Mechanics · Physics 2026-03-23 Enrique P. Cital , Viktor Holubec

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…

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) provide fundamental constraints on the interplay between power fluctuations, entropy production, and efficiency in overdamped stationary autonomous heat engines. However, their validity in…

Statistical Mechanics · Physics 2026-03-23 Enrique P. Cital , Viktor Holubec

The thermodynamic uncertainty relation, which establishes a universal trade-off between nonequilibrium current fluctuations and dissipation, has been found for various Markovian systems. However, this relation has not been revealed for…

Statistical Mechanics · Physics 2019-07-24 Tan Van Vu , Yoshihiko Hasegawa

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

Thermodynamic uncertainty relations (TURs) delineate tradeoff relations between the thermodynamic cost and the magnitude of an observable's fluctuation. While TURs have been established for various nonequilibrium systems, their…

Statistical Mechanics · Physics 2025-06-23 Hyeong-Tark Han , Jae Sung Lee , Jae-Hyung Jeon

We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states, and discuss how optimal these processes are in light of the universal bound set by the thermodynamic…

Biological Physics · Physics 2022-02-28 Yonghyun Song , Changbong Hyeon

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

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

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 theory of stochastic thermodynamics has revealed many useful fluctuation relations, with the thermodynamic uncertainty relation (TUR) being a theorem of major interest. When many nonequilibrium currents interact with each other, a naive…

Statistical Mechanics · Physics 2024-10-16 Michalis Chatzittofi , Ramin Golestanian , Jaime Agudo-Canalejo

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

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

The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied…

Statistical Mechanics · Physics 2022-04-12 Tan Van Vu , Keiji Saito

We investigate a two-qubit SWAP thermal machine -- a streamlined analogue of the four-stroke Otto cycle -- whose working medium comprises inertially moving Unruh-DeWitt qubit detectors, each coupled to a thermal quantum field bath prepared…

Quantum Physics · Physics 2026-03-13 Dimitris Moustos , Obinna Abah

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