A generalized fluctuation relation for power-law distributions
arXiv:1207.2209 · doi:10.1103/PhysRevE.86.011109
Abstract
Strong violations of existing fluctuation theorems may arise in nonequilibrium steady states characterized by distributions with power-law tails. The ratio of the probabilities of positive and negative fluctuations of equal magnitude behaves in an anomalous nonmonotonic way [H. Touchette and E.G.D. Cohen, Phys. Rev. E \textbf{76}, 020101(R) (2007)]. Here, we propose an alternative definition of fluctuation relation (FR) symmetry that, in the power-law regime, is characterized by a monotonic linear behavior. The proposal is consistent with a large deviation-like principle. As example, it is studied the fluctuations of the work done on a dragged particle immersed in a complex environment able to induce power-law tails. When the environment is characterized by spatiotemporal temperature fluctuations, distributions arising in nonextensive statistical mechanics define the work statistics. In that situation, we find that the FR symmetry is solely defined by the average bath temperature. The case of a dragged particle subjected to a Lévy noise is also analyzed in detail.
13 pages, 3 figures
References in corpus (17)
- The large deviation approach to statistical mechanics
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- An Extension of the Fluctuation Theorem
- Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle
- Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces
- Superstatistics, thermodynamics, and fluctuations
- Asymptotics of superstatistics
- Symmetry properties of the large-deviation function of the velocity of a self-propelled polar particle
- Fluctuations of internal energy flow in a vibrated granular gas
- Fluctuations of energy flux in wave turbulence
- Current fluctuations in stochastic systems with long-range memory
- Fluctuation relations for anomalous dynamics
- Fluctuation relation for a Lévy particle
- Fluctuation properties of an effective nonlinear system subject to Poisson noise
- Anomalous fluctuation relations
- Thermodynamics of quantum jump trajectories in systems driven by classical fluctuations
- Fluctuations of energy flux in a simple dissipative out-of-equilibrium system