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Derivation of the Onsager principle from large deviation theory

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  • La Cour, Brian R.
  • Schieve, William C.

Abstract

The Onsager linear relations between macroscopic flows and thermodynamics forces are derived from the point of view of large deviation theory. For a given set of macroscopic variables, we consider the short-time evolution of near-equilibrium fluctuations, represented as the limit of finite-size conditional expectations. The resulting asymptotic conditional expectation is taken to represent the typical macrostate of the system and is used in place of the usual time-averaged macrostate of traditional approaches. By expanding in the short-time, near-equilibrium limit and equating the large deviation rate function with the thermodynamic entropy, a linear relation is obtained between the time rate of change of the macrostate and the conjugate initial macrostate. A Green–Kubo formula for the Onsager matrix is derived and shown to be positive semi-definite, while the Onsager reciprocity relations readily follow from time reversal invariance. Although the initial tendency of a macroscopic variable is to evolve towards equilibrium, we find that this evolution need not be monotonic. The example of an ideal Knundsen gas is considered as an illustration.

Suggested Citation

  • La Cour, Brian R. & Schieve, William C., 2004. "Derivation of the Onsager principle from large deviation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(1), pages 109-124.
    • Handle: RePEc:eee:phsmap:v:331:y:2004:i:1:p:109-124
    DOI: 10.1016/j.physa.2003.09.005
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