# Fluctuation relation for heat engines

@article{Sinitsyn2011FluctuationRF, title={Fluctuation relation for heat engines}, author={Nikolai A. Sinitsyn}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2011}, volume={44} }

We derive the exact equality, referred to as the fluctuation relation for heat engines (FRHE), that relates statistics of heat extracted from one of the two heat baths and the work per one cycle of a heat engine operation. Carnot’s inequality of classical thermodynamics follows as a direct consequence of the FRHE.

## 32 Citations

### Fluctuation relation for quantum heat engines and refrigerators

- Physics
- 2014

At the very foundation of the second law of thermodynamics lies the fact that no heat engine operating between two reservoirs of temperatures TC ⩽ TH can outperform the ideal Carnot engine: 〈W〉/〈QH〉…

### Fluctuation relations for heat engines in time-periodic steady states

- Physics
- 2012

A fluctuation relation for heat engines has been derived recently. In the beginning, the system is in contact with the cooler bath. The system is then coupled to the hotter bath and external…

### Fluctuations in heat engines

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2021

At the dawn of thermodynamics, Carnot’s constraint on efficiency of heat engines stimulated the formulation of one of the most universal physical principles, the second law of thermodynamics. In…

### Carnot heat engine efficiency with a paramagnetic gas

- Physics
- 2019

Considering ideal paramagnetic medium, in this paper we deduced an expression for the thermal efficiency of Carnot heat engine with a paramagnetic gas as working substance. We found that the…

### Dissipation, correlation and lags in heat engines

- Physics
- 2016

By modelling heat engines as driven multi-partite system we show that their dissipation can be expressed in terms of the lag (relative entropy) between the perturbed state of each partition and their…

### Finite-time thermodynamics of fluctuations in microscopic heat engines

- PhysicsPhysical Review Research
- 2022

Fluctuations of thermodynamic quantities become non-negligible and play an important role when the system size is small. We develop finite-time thermodynamics of fluctuations in microscopic heat…

### Nonequilibrium fluctuations of a quantum heat engine

- Physics
- 2021

The thermodynamic properties of quantum heat engines are stochastic owing to the presence of thermal and quantum fluctuations. We here experimentally investigate the efficiency and nonequilibrium…

### Work fluctuation, entropy, and time’s arrow in time-asymmetric engine cycles

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

We derive a thermodynamic uncertainty relation that governs the work yield and the entropy production of an engine operating with a time-asymmetric cycle such as the Carnot cycle. The relation shows…

### Correlation-enhanced stability of microscopic cyclic heat engines

- Engineering, PhysicsPhysical Review Research
- 2022

For cyclic heat engines operating in a ﬁnite cycle period, thermodynamic quantities have intercycle and intracycle correlations. By tuning the driving protocol appropriately, we can get the negative…

### Exchange fluctuation theorems for a chain of interacting particles in presence of two heat baths

- Physics
- 2014

The exchange fluctuation theorem for heat exchanged between two systems at different temperatures, when kept in direct contact, has been investigated by Jarzynski and Wójcik [Phys. Rev. Lett. 92,…

## References

SHOWING 1-10 OF 28 REFERENCES

### Classical and quantum fluctuation theorems for heat exchange.

- PhysicsPhysical review letters
- 2004

The statistics of heat exchange between two classical or quantum finite systems initially prepared at different temperatures are shown to obey a fluctuation theorem.

### Nonequilibrium Equality for Free Energy Differences

- Physics
- 1997

An expression is derived for the equilibrium free energy difference between two configurations of a system, in terms of an ensemble of finite-time measurements of the work performed in parametrically…

### Berry-phase-induced heat pumping and its impact on the fluctuation theorem.

- PhysicsPhysical review letters
- 2010

It is demonstrated that the pumped heat typically exhibits a Berry-phase effect in providing an additional geometric contribution to heat flux, which causes a breakdown of the fluctuation theorem of the Gallavotti-Cohen type for quantum heat transfer.

### Nonequilibrium Measurements of Free Energy Differences for Microscopically Reversible Markovian Systems

- Physics
- 1998

An equality has recently been shown relating the free energy difference between two equilibrium ensembles of a system and an ensemble average of the work required to switch between these two…

### Carnot's cycle for small systems: irreversibility and cost of operations

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

The recently developed framework of the energetics of stochastic processes is employed to reanalyze the Carnot cycle in detail, taking account of fluctuations, and finds that in this nonmacroscopic situation both processes of connection to and disconnection from heat baths and adiabatic processes that cause distortion of the energy distribution are sources of inevitable irreversibility within the cycle.

### Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state

- Physics
- 2005

In a nonequilibrium steady state, the violation of the fluctuation-dissipation theorem (FDT) is connected to breaking detailed balance. For the velocity correlations of a driven colloidal particle we…

### Fluctuations relation and external thermostats: an application to granular materials

- Physics
- 2006

In this paper we discuss a paradigmatic example of interacting particles subject to non-conservative external forces and to the action of thermostats consisting of external (finite) reservoirs of…

### Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics

- Physics, Engineering
- 1981

### Probability of second law violations in shearing steady states.

- MathematicsPhysical review letters
- 1993

An expression for the probability of fluctuations in the shear stress of a fluid in a nonequilibrium steady state far from equilibrium is given and a formula for the ratio that, for a finite time, theShear stress reverse sign is violating the second law of thermodynamics.

### Entropy production in nonequilibrium thermodynamics: a review

- Geology
- 2003

Entropy might be a not well deﬁned concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called “caloric”) in…