# Isometric Uncertainty Relations

@article{Vroylandt2020IsometricUR, title={Isometric Uncertainty Relations}, author={Hadrien Vroylandt and Karel Proesmans and Todd R. Gingrich}, journal={Journal of Statistical Physics}, year={2020}, volume={178}, pages={1039-1053} }

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 bound, which depends on the system’s dimension d , naturally interpolates between two known bounds. The bound derived from the entropy production fluctuation theorem is recovered for $$d=1$$ d = 1 , and the original entropy production thermodynamic uncertainty relation is obtained in the $$d…

## 8 Citations

### Universal Thermodynamic Uncertainty Relation in Non-Equilibrium Dynamics

- Physics
- 2022

We derive a universal thermodynamic uncertainty relation (TUR) that applies to an arbitrary observable in a general Markovian system. The generality of our result allows us to make two ﬁndings: (1)…

### Thermodynamic uncertainty relation for Langevin dynamics by scaling time.

- PhysicsPhysical review. E
- 2022

The thermodynamic uncertainty relation (TUR) quantifies a relationship between current fluctuations and dissipation in out-of-equilibrium overdamped Langevin dynamics, making it a natural counterpart…

### Experimental study of the thermodynamic uncertainty relation

- Physics
- 2019

A cost-precision trade-off relationship, the so-called thermodynamic uncertainty relation (TUR), has been recently discovered in stochastic thermodynamics. It bounds certain thermodynamic observables…

### Thermodynamic uncertainty relation for energy transport in a transient regime: A model study.

- PhysicsPhysical review. E
- 2021

A transient version of the recently discovered thermodynamic uncertainty relation (TUR) which provides a precision-cost trade-off relation for certain out-of-equilibrium thermodynamic observables in terms of net entropy production is investigated and a rigorous proof following the nonequilibrium Green's function approach that the tighter bound is always satisfied in the weak-coupling regime for generic bipartite systems is provided.

### Symmetry-induced fluctuation relations for dynamical observables irrespective of their behavior under time reversal.

- Mathematics, PhysicsPhysical review. E
- 2020

It is proved that given a symmetry at the level of stochastic trajectories in Markov chains, it is always possible to obtain a FR under a biased dynamics corresponding to the so-called generalized Doob transform.

### Precision Enhancement via Symmetry Breaking in Quantum Markov Process

- Physics
- 2021

Symmetry breaking with respect to the time reversal characterizes entropy production. This viewpoint induces us to regard thermodynamic uncertainty relation (TUR), stating that higher precision can…

### Exact statistics and thermodynamic uncertainty relations for a periodically driven electron pump

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

We introduce a model for a periodically driven electron pump that sequentially interacts with an arbitrary number of heat and particle reservoirs. Exact expressions for the thermodynamic fluxes, such…

### Multilevel quantum thermodynamic swap engines

- Physics, EngineeringPhysical Review A
- 2021

We study energetic exchanges and fluctuations in two-stroke quantum thermodynamic engines where the working fluid is represented by two multilevel quantum systems, i.e. qudits, the heat flow is…

## References

SHOWING 1-10 OF 34 REFERENCES

### Thermodynamic Uncertainty Relations from Exchange Fluctuation Theorems.

- PhysicsPhysical review letters
- 2019

This Letter identifies the tightest (and saturable) matrix-valued TUR that can be derived from the exchange fluctuation theorems describing the statistics of heat and particle flow between multiple systems of arbitrary dimensions.

### Fluctuation Theorem Uncertainty Relation.

- PhysicsPhysical review letters
- 2019

It is shown that the fluctuation theorem uncertainty relation can handle systems controlled by time-symmetric external protocols, in which the lower bound is given by the work exerted on the systems.

### Multidimensional thermodynamic uncertainty relations

- EconomicsJournal of Physics A: Mathematical and Theoretical
- 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…

### Thermodynamic uncertainty relations constrain non-equilibrium fluctuations

- PhysicsNature Physics
- 2019

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…

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

- Physics
- 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…

### Thermodynamic uncertainty relations including measurement and feedback.

- PhysicsPhysical 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.

### Isometric fluctuation relations for equilibrium states with broken symmetry.

- PhysicsPhysical review letters
- 2014

A set of isometric fluctuation relations are derived, which constrain the order parameter fluctuations in finite-size systems at equilibrium and in the presence of a broken symmetry, which apply generally to many condensed-matter physics systems.

### Fluctuation relations for equilibrium states with broken discrete symmetries

- Physics
- 2012

Relationships are obtained expressing the breaking of spin-reversal symmetry by an external magnetic field in Gibbsian canonical equilibrium states of spin systems under specific assumptions. These…

### Assessing the validity of the thermodynamic uncertainty relation in quantum systems

- PhysicsPhysical Review B
- 2018

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…

### Symmetries in fluctuations far from equilibrium

- PhysicsProceedings of the National Academy of Sciences
- 2011

An isometric fluctuation relation is derived that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations, and this relation adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations.