A field-theoretic approach to nonequilibrium work identities

Abstract

We study nonequilibrium work relations for a space-dependent field with stochastic dynamics (Model A). Jarzynski's equality is obtained through symmetries of the dynamical action in the path integral representation. We derive a set of exact identities that generalize the fluctuation-dissipation relations to non-stationary and far-from-equilibrium situations. These identities are prone to experimental verification. Furthermore, we show that a well-studied invariance of the Langevin equation under supersymmetry, which is known to be broken when the external potential is time-dependent, can be partially restored by adding to the action a term which is precisely Jarzynski's work. The work identities can then be retrieved as consequences of the associated Ward-Takahashi identities.

15 pages

References in corpus (23)

• A nonequilibrium equality for free energy differences
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Fluctuation theorem for stochastic dynamics
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Path ensembles averages in systems driven far-from-equilibrium
• Riemannian symmetric superspaces and their origin in random matrix theory
• Quantum Field Theory in the Large N Limit: a review
• Fluctuations and response of nonequilibrium states
• Rare events and the convergence of exponentially averaged work values
• Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
• A fluctuation theorem for currents and non-linear response coefficients
• Fluctuation Relations for Diffusion Processes
• On practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example
• Supersymmetry for Systems with Unitary Disorder: Circular Ensembles
• Fluctuation relations in simple examples of non-equilibrium steady states
• Reexamination of experimental tests of the fluctuation theorem
• Estimate of the free energy difference in mechanical systems from work fluctuations: experiments and models
• Jarzynski equality for the Jepsen gas
• Eulerian and Lagrangian pictures of non-equilibrium diffusions
• Generalized Einstein or Green-Kubo relations for active biomolecular transport
• Non-Equilibrium Thermodynamics and Topology of Currents
• Geometrical phases and quantum numbers of solitons in nonlinear sigma-models

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• Fluctuation Relation for Heat
• Dynamical symmetry approach and topological field theory for path integrals of quantum spin systems
• Emergent Supersymmetry in Local Equilibrium Systems
• Multiple dynamic transitions in nonequilibrium work fluctuations
• An Inflow Mechanism for Hydrodynamic Entropy
• Quantum-classical correspondence principle for heat distribution in quantum Brownian motion
• Fluctuation Dissipation Relations for Active Field Theories
• Symmetry and its breaking in path integral approach to quantum Brownian motion
• Promoting Fluctuation Theorems into Covariant Forms
• Supersymmetries in non-equilibrium Langevin dynamics
• Nonequilibrium thermodynamics perspectives for the monotonicity of the renormalization group flow
• A note on symmetries in the path integral formulation of the Langevin dynamics
• Series expansion of the excess work using nonlinear response theory
• Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold
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