# Random paths and current fluctuations in nonequilibrium statistical mechanics

## Abstract

An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is considered in time or spacetime for nonequilibrium systems. In this approach, relationships have been established between nonequilibrium properties such as the transport coefficients, the thermodynamic entropy production, or the affinities, and quantities characterizing the microscopic Hamiltonian dynamics and the chaos or fluctuations it may generate. This overview presents results for classical systems in the escape-rate formalism, stochastic processes, and open quantum systems.

- Authors:

- Center for Nonlinear Phenomena and Complex Systems and Department of Physics, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels (Belgium)

- Publication Date:

- OSTI Identifier:
- 22306196

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 7; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; EQUILIBRIUM; FLUCTUATIONS; RANDOMNESS; SPACE-TIME; STATISTICAL MECHANICS; STATISTICS; STOCHASTIC PROCESSES

### Citation Formats

```
Gaspard, Pierre.
```*Random paths and current fluctuations in nonequilibrium statistical mechanics*. United States: N. p., 2014.
Web. doi:10.1063/1.4881534.

```
Gaspard, Pierre.
```*Random paths and current fluctuations in nonequilibrium statistical mechanics*. United States. doi:10.1063/1.4881534.

```
Gaspard, Pierre. Tue .
"Random paths and current fluctuations in nonequilibrium statistical mechanics". United States.
doi:10.1063/1.4881534.
```

```
@article{osti_22306196,
```

title = {Random paths and current fluctuations in nonequilibrium statistical mechanics},

author = {Gaspard, Pierre},

abstractNote = {An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is considered in time or spacetime for nonequilibrium systems. In this approach, relationships have been established between nonequilibrium properties such as the transport coefficients, the thermodynamic entropy production, or the affinities, and quantities characterizing the microscopic Hamiltonian dynamics and the chaos or fluctuations it may generate. This overview presents results for classical systems in the escape-rate formalism, stochastic processes, and open quantum systems.},

doi = {10.1063/1.4881534},

journal = {Journal of Mathematical Physics},

number = 7,

volume = 55,

place = {United States},

year = {Tue Jul 15 00:00:00 EDT 2014},

month = {Tue Jul 15 00:00:00 EDT 2014}

}

DOI: 10.1063/1.4881534

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