Generalized Jarzynski equality under nonequilibrium feedback control.

  title={Generalized Jarzynski equality under nonequilibrium feedback control.},
  author={Takahiro Sagawa and Masahito Ueda},
  journal={Physical review letters},
  volume={104 9},
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… 

Figures from this paper

Nonequilibrium thermodynamics of feedback control.

A general theory of feedback control on classical stochastic thermodynamic systems is established and nonequilibrium equalities such as the fluctuation theorem and the Jarzynski equality are generalized.

Hamiltonian Derivations of the Generalized Jarzynski Equalities under Feedback Control

In the presence of feedback control by "Maxwell's demon," the second law of thermodynamics and the nonequilibrium equalities such as the Jarzynski equality need to be generalized. In this paper, we

Entropy production and fluctuation theorems under feedback control: the molecular refrigerator model revisited

We revisit the model of a Brownian particle in a heat bath submitted to an actively controlled force proportional to the velocity that leads to thermal noise reduction (cold damping). We investigate

Entropy production and fluctuation theorems for Langevin processes under continuous non-Markovian feedback control.

A new definition of the quantity measuring the irreversibility of a path in a nonequilibrium stationary state is proposed, which can also be regarded as the trajectory-dependent total entropy production, which leads to an extension of the second law.

Stochastic thermodynamics based on incomplete information: generalized Jarzynski equality with measurement errors with or without feedback

In the derivation of fluctuation relations, and in stochastic thermodynamics in general, it is tacitly assumed that we can measure the system perfectly, i.e., without measurement errors. We here

Fluctuation theorem with information exchange: role of correlations in stochastic thermodynamics.

The fluctuation theorem is established in the presence of information exchange between a nonequilibrium system and other degrees of freedom such as an observer and a feedback controller, and the resulting generalized second law sets the fundamental limit of energy dissipation and energy cost during the information exchange.

Information fluctuation theorem for an open quantum bipartite system.

This work presents a fluctuation theorem (FT) that explicitly addresses the quantum correlation of subsystems during the thermodynamic evolution and derives a FT in such a form that relates the entropy production of local systems in the time-forward transition to the change of quantum correlation in theTime-reversed transition.

Uncertainty relation under information measurement and feedback control

It is proved that the entropy production and the information quantity constrain from below the fluctuation of arbitrary observables that are antisymmetric under time reversal.

Perpetual extraction of work from a nonequilibrium dynamical system under Markovian feedback control.

  • Taichi Kosugi
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2013
A succinct theory of perpetual extraction of work from a generic classical nonequilibrium system subject to a heat bath via repeated measurements under a Markovian feedback control is developed and a version of the detailed fluctuation theorem is derived.

Quantum nonequilibrium equalities with absolute irreversibility

We derive quantum nonequilibrium equalities in absolutely irreversible processes. Here by absolute irreversibility we mean that in the backward process the density matrix does not return to the



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.