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The thermodynamic uncertainty relation is a universal trade-off relation connecting the precision of a current with the average dissipation at large times. For continuous time Markov chains (also called Markov jump processes) this relation…

Statistical Mechanics · Physics 2019-09-04 A. C. Barato , R. Chetrite , A. Faggionato , D. Gabrielli

Nanoscale heat engines are subject to large fluctuations which affect their precision. The Thermodynamic Uncertainty Relation (TUR) provides a trade-off between output power, fluctuations and entropic cost. This trade-off may be overcome by…

Quantum Physics · Physics 2021-08-04 Alex Arash Sand Kalaee , Andreas Wacker , Patrick P. Potts

Autonomous engines operating at the nano-scale can be prone to deleterious fluctuations in the heat and particle currents which increase, for fixed power output, the more reversible the operation regime is. This fundamental trade-off…

Statistical Mechanics · Physics 2019-10-23 Giacomo Guarnieri , Gabriel T. Landi , Stephen R. Clark , John Goold

The thermodynamic uncertainty relations (TURs), originally discovered for classical systems, dictate the trade-off between dissipation and fluctuations of irreversible current, specifying a minimal bound that constrains the two quantities.…

Quantum Physics · Physics 2022-02-28 Davinder Singh , Changbong Hyeon

We derive a thermodynamic uncertainty relation (TUR) under quantum continuous measurement and feedback control. By incorporating the quantum-classical-transfer entropy, which quantifies the information gained by continuous measurement, we…

Statistical Mechanics · Physics 2026-03-20 Kaito Tojo , Takahiro Sagawa , Ken Funo

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

Fluctuations affect the functionality of nanodevices. Thermodynamic uncertainty relations (TURs), derived within the framework of stochastic thermodynamics, show that a minimal amount of dissipation is required to obtain a given relative…

Quantum Physics · Physics 2024-09-13 Luca Razzoli , Matteo Carrega , Fabio Cavaliere , Giuliano Benenti , Maura Sassetti

We demonstrate that the charge value of transport mechanisms heavily impacts the validity of thermodynamic uncertainty relations (TURs). Specifically, we show within the framework of full counting statistics, that the recently established…

Mesoscale and Nanoscale Physics · Physics 2025-12-24 David Christian Ohnmacht , Wolfgang Belzig , Juan Carlos Cuevas

The putative generalization of the thermodynamic uncertainty relation (TUR) to underdamped dynamics is still an open problem. So far, bounds that have been derived for such a dynamics are not particularly transparent and they do not…

Statistical Mechanics · Physics 2020-07-15 Lukas P. Fischer , Hyun-Myung Chun , Udo Seifert

We consider a Brownian particle in harmonic confinement of stiffness $k$, in one dimension in the underdamped regime. The whole setup is immersed in a heat bath at temperature $T$. The center of harmonic trap is dragged under any arbitrary…

Statistical Mechanics · Physics 2020-03-18 Deepak Gupta , Amos Maritan

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 thermodynamics and kinetics of a nonequilibrium classical system fundamentally constrain the precision of an observable regarding the celebrated thermodynamic uncertainty relation (TUR) and the kinetic uncertainty relation (KUR). They…

Quantum Physics · Physics 2025-01-10 Kangqiao Liu , Jie Gu

We investigate fundamental limits on the performance of information processing systems from the perspective of information thermodynamics. We first extend the thermodynamic uncertainty relation (TUR) to a subsystem. Specifically, for a…

Statistical Mechanics · Physics 2024-01-04 Tomohiro Tanogami , Tan Van Vu , Keiji Saito

We investigate the tightness and optimality of thermodynamic-uncertainty-relation (TUR)-type inequalities from two aspects, the choice of the Fisher information and the class of possible observables. We show that there exists the best…

Statistical Mechanics · Physics 2023-04-26 Naoto Shiraishi

We introduce a continuous time-reversal operation which connects the time-forward and time-reversed trajectories in the steady state of an irreversible Markovian dynamics via a continuous family of stochastic dynamics. This continuous…

Statistical Mechanics · Physics 2022-01-10 Andreas Dechant , Shin-ichi Sasa

The thermodynamic uncertainty relation expresses a universal trade-off between precision and entropy production, which applies in its original formulation to current observables in steady-state systems. We generalize this relation to…

Statistical Mechanics · Physics 2018-12-06 Timur Koyuk , Udo Seifert , Patrick Pietzonka

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

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 yield a lower bound on entropy production in terms of the mean and fluctuations of a current. We derive their general form for systems under arbitrary time-dependent driving from arbitrary initial states…

Statistical Mechanics · Physics 2021-01-12 Timur Koyuk , Udo Seifert

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