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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) are recently established relations between the relative uncertainty of time-integrated currents and entropy production in nonequilibrium systems. For small perturbations away from equilibrium,…

Statistical Mechanics · Physics 2018-10-05 Katarzyna Macieszczak , Kay Brandner , Juan P. Garrahan

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 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

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

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

The precision of currents in Markov networks is bounded by dissipation via the so-called thermodynamic uncertainty relation (TUR). In our work, we demonstrate a similar inequality that bounds the precision of the static current response to…

Statistical Mechanics · Physics 2024-11-26 Krzysztof Ptaszynski , Timur Aslyamov , Massimiliano Esposito

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

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 (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

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 the thermodynamic uncertainty relation (TUR), \textit{i.e.} a trade-off between entropy production rate and relative power fluctuations, for nondegenerate three-level and degenerate four-level maser heat engines. In the…

Quantum Physics · Physics 2022-12-19 Varinder Singh , Vahid Shaghaghi , Özgür E. Müstecaplıoğlu , Dario Rosa

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

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

Feedback cooling enables a system to achieve low temperatures through measurement-based control. Determining the thermodynamic cost required to achieve the ideal cooling efficiency within a finite time remains an important problem. In this…

Statistical Mechanics · Physics 2025-12-02 Kousuke Kumasaki , Kaito Tojo , Takahiro Sagawa , Ken Funo

Recently, it has been shown that there is a trade-off relation between thermodynamic cost and current fluctuations, referred to as the thermodynamic uncertainty relation (TUR). The TUR has been derived for various processes, such as…

Statistical Mechanics · Physics 2020-01-01 Jae Sung Lee , Jong-Min Park , Hyunggyu Park

The kinetic uncertainty relation (KUR) is a trade-off relation between the precision of an observable and the mean dynamical activity in a fixed time interval for a time-homogeneous and continuous-time Markov chain. In this letter, we…

Statistical Mechanics · Physics 2021-05-26 Ken Hiura , Shin-ichi Sasa

Thermodynamic (TUR) and kinetic (KUR) uncertainty relations are fundamental bounds constraining the fluctuations of current observables in classical, non-equilibrium systems. Several works have verified, however, violations of these…

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

Entropy production characterizes the thermodynamic irreversibility and reflects the amount of heat dissipated into the environment and free energy lost in nonequilibrium systems. According to the thermodynamic uncertainty relation, we…

Statistical Mechanics · Physics 2020-05-01 Tan Van Vu , Van Tuan Vo , Yoshihiko Hasegawa