# Thermodynamic uncertainty relations constrain non-equilibrium fluctuations

@article{Horowitz2019ThermodynamicUR, title={Thermodynamic uncertainty relations constrain non-equilibrium fluctuations}, author={Jordan M. Horowitz and Todd R. Gingrich}, journal={Nature Physics}, year={2019}, volume={16}, pages={15-20} }

In equilibrium thermodynamics, there exists a well-established connection between dynamical fluctuations of a physical system and the dissipation of its energy into an environment. However, few similarly quantitative tools are available for the description of physical systems out of equilibrium. Here, we offer our perspective on the recent development of a new class of inequalities known as thermodynamic uncertainty relations, which have revealed that dissipation constrains current fluctuations… Expand

#### Figures from this paper

#### 99 Citations

Comment on the perspective article "Thermodynamic uncertainty relations constrain non-equilibrium fluctuations"

- Computer Science, Physics
- 2020

How the principle of microscopic reversibility reveals that the true origin of directional cycling amongst a network of states is kinetic asymmetry is illustrated. Expand

Improving thermodynamic bounds using correlations

- Physics
- 2021

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… Expand

Nonequilibrium Thermodynamics in Biochemical Systems and Its Application

- Computer Science, Medicine
- Entropy
- 2021

The history and current development of nonequilibrium thermodynamics, especially that in biochemical systems, are introduced and the development of stochastic thermodynamics is introduced, especially three landmarks: Jarzynski equality, Crooks’ fluctuation theorem and thermodynamic uncertainty relation. Expand

The origin of loose bound of the thermodynamic uncertainty relation in a dissipative two-level quantum system

- Physics
- 2021

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

Thermodynamic speed limits from the regression of information

- Physics
- 2021

Irreversible processes accomplished in a fixed time involve nonlinearly coupled flows of matter, energy, and information. Here, using entropy production as an example, we show how thermodynamic… Expand

Isometric Uncertainty Relations

- Physics, Mathematics
- 2019

We generalize the link between fluctuation theorems and thermodynamic uncertainty relations by deriving a bound on the variance of fluxes that satisfy an isometric fluctuation theorem. The resulting… Expand

Universal dynamic scaling in chemical reactions at and away from equilibrium

- Physics
- 2021

Physical kinetic roughening processes are well known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the… Expand

Stochastic thermodynamics and fluctuation theorems for non-linear systems

- Physics, Mathematics
- 2020

We extend stochastic thermodynamics by relaxing the two assumptions that the Markovian dynamics must be linear and that the equilibrium distribution must be a Boltzmann distribution. We show that if… Expand

Quantitative analysis of non-equilibrium systems from short-time experimental data

- Physics
- 2021

We provide a \textit{minimal} strategy for the quantitative analysis of a large class of non-equilibrium systems in a steady state using the short-time Thermodynamic Uncertainty Relation (TUR). From… Expand

Thermodynamic uncertainty relation in the overdamped limit with a magnetic Lorentz force

- Physics
- 2021

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… Expand

#### References

SHOWING 1-10 OF 63 REFERENCES

Unified Thermodynamic Uncertainty Relations in Linear Response.

- Physics, Medicine
- Physical review letters
- 2018

This work uses linear response theory to deriveThermodynamic uncertainty relations (TURs) in a straightforward and unified way and finds that, for broken time reversal, the bounds on the relative uncertainty are controlled both by dissipation and by a parameter encoding the asymmetry of the Onsager matrix. Expand

Thermodynamic bounds on equilibrium fluctuations of a global or local order parameter

- Physics, Mathematics
- 2016

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… Expand

Kinetic uncertainty relation

- Physics, Mathematics
- 2018

The approach is based on the recent fluctuation response inequality by Dechant and Sasa and can be applied to generic Markov jump systems, which describe a wide class of phenomena and observables, including the irreversible predator-prey dynamics that is used as an illustration. Expand

Finite-time generalization of the thermodynamic uncertainty relation.

- Mathematics, Physics
- Physical review. E
- 2017

It is shown that this relation holds not only for the long-time limit of fluctuations, as described by large deviation theory, but also for fluctuations on arbitrary finite time scales, which facilitates applying the thermodynamic uncertainty relation to single molecule experiments, for which infinite time scales are not accessible. Expand

Multidimensional thermodynamic uncertainty relations

- Mathematics, Physics
- 2018

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… Expand

Universal Thermodynamic Bounds on Nonequilibrium Response with Biochemical Applications

- Physics, Biology
- 2019

A collection of equalities and inequalities valid arbitrarily far from equilibrium that constrain the response ofNonequilibrium steady states in terms of the strength of nonequilibrium driving are derived. Expand

Proof of the finite-time thermodynamic uncertainty relation for steady-state currents.

- Physics, Mathematics
- Physical review. E
- 2017

This work proves a recently conjectured finite-time thermodynamic uncertainty relation for steady-state current fluctuations based on a quadratic bound to the large deviation rate function for currents in the limit of a large ensemble of many copies. Expand

A generalization of the thermodynamic uncertainty relation to periodically driven systems

- Mathematics, Physics
- 2018

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… Expand

Thermodynamic uncertainty relations including measurement and feedback.

- Medicine, Physics
- Physical review. E
- 2019

Thermodynamic uncertainty relations quantify how the signal-to-noise ratio of a given observable is constrained by dissipation and show that any fluctuation relation directly implies a thermodynamic uncertainty relation, considerably increasing their range of applicability. Expand

A unifying picture of generalized thermodynamic uncertainty relations.

- Mathematics, Physics
- 2018

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… Expand