# Fluctuation relation for heat engines

@article{Sinitsyn2011FluctuationRF, title={Fluctuation relation for heat engines}, author={Nikolai A Sinitsyn}, journal={Journal of Physics A}, year={2011}, volume={44}, pages={405001} }

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.

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#### References

SHOWING 1-10 OF 47 REFERENCES

Classical and quantum fluctuation theorems for heat exchange.

- Physics, Medicine
- Physical 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… Expand

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

- Physics, Medicine
- Physical 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. Expand

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… Expand

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

- Mathematics, Medicine
- Physical 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. Expand

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… Expand

Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics

- Physics
- 1981

The paper is devoted to the theory of thermal fluctuations in nonlinear macroscopic systems and to the derivation of variational principles of nonlinear nonequilibrium thermodynamics. In the first… Expand

Fluctuations relation and external thermostats: an application to granular materials

- Mathematics
- 2006

In this note 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… Expand

Probability of second law violations in shearing steady states.

- Physics, Medicine
- Physical 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. Expand

Stochastic thermodynamics and sustainable efficiency in work production.

- Physics, Medicine
- Physical review letters
- 2010

A novel definition of efficiency, valid for motors in a nonequilibrium stationary state exchanging heat and possibly other resources with an arbitrary number of reservoirs, implies that at maximum power bithermal, stationary motors could reach a higher Carnot efficiency than the usual cyclic motors. Expand