Thermodynamic and stochastic theory of nonequilibrium systems: A Lagrangian approach to fluctuations and relation to excess work

Suárez, Alberto; Ross, John; Peng, Bo; Hunt, Katharine L. C.; Hunt, Paul M.
March 1995
Journal of Chemical Physics;3/15/1995, Vol. 102 Issue 11, p4563
Academic Journal
The dynamics of fluctuations in systems approaching a nonequilibrium steady state, with or without detailed balance, are investigated by means of a Lagrangian function, which is derived from the generator of time displacement (Hamiltonian) of the mesoscopic evolution equation. In the thermodynamic limit, the stationary probability distribution for the fluctuating variables is expressed in terms of the action of this stochastic Lagrangian along the fluctuational trajectory, the most probable path of infinite duration for the generation of a particular fluctuation away from the steady state. The fluctuational trajectory is related by a gaugelike transformation to the deterministic trajectory, which is the most probable path for the relaxation of the macroscopic system to the steady state. This framework is applied to the analysis of one-variable chemical reactions modeled by a constant step master equation, and to two-variable systems in the linearized region around the steady state, where the fluctuations are described by a linear Fokker–Planck equation. In these examples, the thermodynamic significance of the action along the fluctuational trajectory is established by relating the irreversible (odd under time inversion) part of the Lagrangian and the time derivative of a deterministic excess work. © 1995 American Institute of Physics.


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