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.


Related Articles

  • Thermodynamic and stochastic theory of nonequilibrium systems: Fluctuation probabilities and excess work. Peng, Bo; Hunt, Katharine L. C.; Hunt, Paul M.; Suárez, Alberto; Ross, John // Journal of Chemical Physics;3/15/1995, Vol. 102 Issue 11, p4548 

    For a nonequilibrium system described at the mesoscopic level by the master equation, we prove that the probability of fluctuations about a steady state is governed by a thermodynamic function, the ‘‘excess work.’’ The theory applies to systems with one or more...

  • Nonequilibrium work relations: foundations and applications. Jarzynskia, C. // European Physical Journal B -- Condensed Matter;Jul2008, Vol. 64 Issue 3/4, p331 

    When a macroscopic system in contact with a heat reservoir is driven away from equilibrium, the second law of thermodynamics places a strict bound on the amount of work performed on the system. With a microscopic system the situation is more subtle, as thermal fluctuations give rise to a...

  • Lagrangian modeling of scalar statistics in a double scalar mixing layer. Sawford, Brian L. // Physics of Fluids;Aug2006, Vol. 18 Issue 8, p085108 

    Statistics of scalar concentration in a double scalar mixing layer are calculated using a Lagrangian stochastic model coupled to the interaction by exchange with the conditional mean micromixing model. Excellent agreement is obtained with recent direct numerical simulation results. The model...

  • On the Physical Origin of Long-Ranged Fluctuations in Fluids in Thermal Nonequilibrium States. Ortiz de Zárate, José M.; Sengers, Jan V. // Journal of Statistical Physics;Jun2004, Vol. 115 Issue 5/6, p1341 

    Thermodynamic fluctuations in systems that are in nonequilibrium steady states are always spatially long ranged, in contrast to fluctuations in thermodynamic equilibrium. In the present paper we consider a fluid subjected to a stationary temperature gradient. Two different physical mechanisms...

  • Temporal asymmetry of fluctuations in nonequilibrium steady states. Paneni, Carlo; Searles, Debra J.; Rondoni, Lamberto // Journal of Chemical Physics;3/21/2006, Vol. 124 Issue 11, p114109 

    Temporal asymmetries of fluctuation paths in nonequilibrium microscopic shearing systems are observed for the first time. Inspired by theories that predict asymmetry of fluctuation paths in stochastic dynamics, we focus on deterministic reversible particle models, which represent a small part of...

  • Exact results for the 1D asymmetric exclusion process and KPZ fluctuations. Sasamoto, T. // European Physical Journal B -- Condensed Matter;Jul2008, Vol. 64 Issue 3/4, p373 

    We discuss several properties of the current of the one-dimensional asymmetric simple exclusion process (ASEP) through exact solutions. First we explain the stationary measure for the finite system with boundaries and its average current. Then we study the fluctuation properties of the current...

  • Fluctuation theorem and chaos. Gallavottia, G. // European Physical Journal B -- Condensed Matter;Jul2008, Vol. 64 Issue 3/4, p315 

    The heat theorem (i.e. the second law of thermodynamics or the existence of entropy) is a manifestation of a general property of hamiltonian mechanics and of the ergodic hypothesis. In nonequilibrium thermodynamics of stationary states the chaotic hypothesis plays a similar role: it allows a...

  • Unfying approach for fluctuation theorems from joint probability distributions. García-García, Reinaldo; Domínguez, D.; Lecomte, Vivien; Kolton, A. B. // AIP Conference Proceedings;3/24/2011, Vol. 1332 Issue 1, p277 

    Any decomposition of the total trajectory entropy production for markovian systems have a joint probability distribution satisfying a generalized detailed fluctuation theorem, without relying in dual probability distributions, when all the contributing terms are odd with respect to time...

  • An Information Theory Approach to Nonlinear, Nonequilibrium Thermodynamics. Rogers, David; Beck, Thomas; Rempe, Susan // Journal of Statistical Physics;Oct2011, Vol. 145 Issue 2, p385 

    Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complex thermodynamic models by successively adding physical information. We present a new formulation of information algebra that generalizes methods of both information theory and statistical...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics