Computation of Current Cumulants for Small Nonequilibrium Systems

@article{Baiesi2009ComputationOC,
  title={Computation of Current Cumulants for Small Nonequilibrium Systems},
  author={Marco Baiesi and Christian Maes and Karel Netocny},
  journal={Journal of Statistical Physics},
  year={2009},
  volume={135},
  pages={57-75}
}
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-Schrödinger 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… Expand

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References

SHOWING 1-10 OF 140 REFERENCES
Universal cumulants of the current in diffusive systems on a ring.
TLDR
This work calculates exactly the first cumulants of the integrated current and of the activity of the symmetric simple exclusion process on a ring with periodic boundary conditions and indicates that for large system sizes the large deviation functions of the current and the activity take a universal scaling form. Expand
A Selection of Nonequilibrium Issues
We give a pedagogical introduction to a selection of recently discussed topics in nonequilibrium statistical mechanics, concentrating mostly on formal structures and on general principles. Part IExpand
Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states
We give the explicit structure of the functional governing the dynamical density and current fluctuations for a mesoscopic system in a nonequilibrium steady state. Its canonical form determines aExpand
Stochastic path integral formulation of full counting statistics.
TLDR
A stochastic path integral representation of counting statistics in semiclassical systems is derived and the current cumulants of a chaotic cavity in the hot-electron regime are derived. Expand
Mesoscopic full counting statistics and exclusion models
Abstract.We calculate the distribution of current fluctuations in two simple exclusion models. Although these models are classical, we recover even for small systems such as a simple or a doubleExpand
Non Equilibrium Current Fluctuations in Stochastic Lattice Gases
We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a largeExpand
Counting statistics of non-Markovian quantum stochastic processes.
TLDR
A general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes is derived and the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise are studied. Expand
Current Fluctuations in the One-Dimensional Symmetric Exclusion Process with Open Boundaries
We calculate the first four cumulants of the integrated current of the one-dimensional symmetric simple exclusion process of N sites with open boundary conditions. For large system size N, theExpand
Distribution of current in nonequilibrium diffusive systems and phase transitions.
  • T. Bodineau, B. Derrida
  • Physics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
TLDR
This time dependent profile persists in the large drift limit and allows one to understand on physical grounds the results obtained earlier for the totally asymmetric exclusion process on a ring. Expand
Large Deviations for the Boundary Driven Symmetric Simple Exclusion Process
The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in nonequilibrium, namely for nonreversible systems. In thisExpand
...
1
2
3
4
5
...