Generalized Jarzynski equality under nonequilibrium feedback control.

@article{Sagawa2009GeneralizedJE,
  title={Generalized Jarzynski equality under nonequilibrium feedback control.},
  author={Takahiro Sagawa and Masahito Ueda},
  journal={Physical review letters},
  year={2009},
  volume={104 9},
  pages={
          090602
        }
}
The Jarzynski equality is generalized to situations in which nonequilibrium systems are subject to a feedback control. The new terms that arise as a consequence of the feedback describe the mutual information content obtained by measurement and the efficacy of the feedback control. Our results lead to a generalized fluctuation-dissipation theorem that reflects the readout information, and they can be experimentally tested using small thermodynamic systems. We illustrate our general results by… 
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References

SHOWING 1-10 OF 41 REFERENCES

Fluctuation theorems for a molecular refrigerator.

  • K. KimH. Qian
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
The presence of entropy pumping in an underdamped Brownian system modifies both the Jarzynski equality and the fluctuation theorems and it is discovered that the entropy pumping has a dual role of work and heat.

Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences.

  • G. Crooks
  • Economics, Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1999
A generalized version of the fluctuation theorem is derived for stochastic, microscopically reversible dynamics and this generalized theorem provides a succinct proof of the nonequilibrium work relation.

Second law of thermodynamics with discrete quantum feedback control.

A new thermodynamic inequality is derived which leads to the maximum work that can be extracted from multi-heat-baths with the assistance of discrete quantum feedback control, and this maximum work can exceed that in conventional thermodynamics.

Steady-state thermodynamics of Langevin systems.

L Langevin dynamics describing nonequilibirum steady states is studied, finding that the extended form of the second law which they proposed holds for transitions between steady states and that the Shannon entropy difference is related to the excess heat produced in an infinitely slow operation.

Thermodynamics of feedback controlled systems.

We compute the entropy reduction in feedback controlled systems due to the repeated operation of the controller. This was the lacking ingredient to establish the thermodynamics of these systems, and…

Dynamical Ensembles in Nonequilibrium Statistical Mechanics.

This presents the first test of the Ruelle principle on a many particle system far from equilibrium, and a specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid.

Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski's Equality

The implementation and test of Jarzynski's equality provides the first example of its use as a bridge between the statistical mechanics of equilibrium and nonequilibrium systems, and extends the thermodynamic analysis of single molecule manipulation data beyond the context of equilibrium experiments.

Realization of a feedback controlled flashing ratchet.

A flashing ratchet that uses feedback to increase velocity is experimentally realized using an optical line trap, and it is observed that use of feedback increases velocity by up to an order of magnitude.

Dissipation: the phase-space perspective.

It is shown that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by =W-DeltaF=kTD(rho||rho[ over ])=kT, where rho and rho[over ] are the phase-space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward and backward process.

Experimental test of a new equality: measuring heat dissipation in an optically driven colloidal system.

This work shows an experimental test of an equality relating the energy dissipation rate to experimentally accessible quantities in nonequilibrium steady states described by the Langevin equation, and finds that this equality is validated to a fairly good extent, thus the irreversible work of a small system is estimated from readily obtainable quantities.