### Abstract

We reconsider a well-known relationship between the fluctuation theorem and the second law of thermodynamics by evaluating stochastic evolution of the density field (probability measure valued process). In order to establish a bridge between microscopic and macroscopic behaviors, we must take the thermodynamic limit of a stochastic dynamical system following the standard procedure in statistical mechanics. The thermodynamic path characterizing a dynamical behavior in the macroscopic scale can be formulated as an infimum of the action functional for the stochastic evolution of the density field. In our formulation, the second law of thermodynamics can be derived only by symmetry of the action functional without recourse to the Jarzynski equality. Our formulation leads to a nontrivial nonequilibrium work relation for metastable (quasi-stationary) states, which are peculiar in the macroscopic system. We propose a prescription for computing the free energy for metastable states based on the resultant work relation.

Original language | English |
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Article number | P04012 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2013 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2013 Apr 1 |

Externally published | Yes |

### Keywords

- driven diffusive systems (theory)
- large deviations in non-equilibrium systems
- metastable states
- stochastic particle dynamics (theory)

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2013*(4), [P04012]. https://doi.org/10.1088/1742-5468/2013/04/P04012