TY - JOUR

T1 - Nonequilibrium work relation in a macroscopic system

AU - Sughiyama, Yuki

AU - Ohzeki, Masayuki

PY - 2013/4

Y1 - 2013/4

N2 - 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.

AB - 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.

KW - driven diffusive systems (theory)

KW - large deviations in non-equilibrium systems

KW - metastable states

KW - stochastic particle dynamics (theory)

UR - http://www.scopus.com/inward/record.url?scp=84876936990&partnerID=8YFLogxK

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U2 - 10.1088/1742-5468/2013/04/P04012

DO - 10.1088/1742-5468/2013/04/P04012

M3 - Article

AN - SCOPUS:84876936990

SN - 1742-5468

VL - 2013

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 4

M1 - P04012

ER -