Computation of current cumulants for small nonequilibrium systems

Abstract

We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on identifying the current cumulants from a Rayleigh-Schrodinger perturbation expansion for the generating function. Here it is derived from a simple path-distribution identity and extended to the joint statistics of multiple currents. For a possible thermodynamical interpretation, we compare this approach to a generalized Onsager-Machlup formalism. We present calculations for a boundary driven Kawasaki dynamics on a one-dimensional chain, both for attractive and repulsive particle interactions.

v2: accepted in J.Stat.Phys, appendix added, 19 pages, 2 figures

References in corpus (15)

• Counting Statistics of Non-Markovian Quantum Stochastic Processes
• Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states
• Universal cumulants of the current in diffusive systems on a ring
• A numerical approach to large deviations in continuous-time
• Full counting statistics of nano-electromechanical systems
• Steady state statistics of driven diffusions
• Cumulants and large deviations of the current through non-equilibrium steady states
• Detection of non-Gaussian Fluctuations in a Quantum Point Contact
• Large deviation function for entropy production in driven one-dimensional systems
• On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
• A selection of nonequilibrium issues
• Reflection positivity and phase transitions in lattice spin models
• Thermodynamic formalism and large deviation functions in continuous time Markov dynamics
• Full counting statistics of spin transfer through ultrasmall quantum dots
• Quantum detectors for the third cumulant of current fluctuations

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