Derivation of the Onsager principle from large deviation theory

✍ Scribed by Brian R. La Cour; William C. Schieve

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 258 KB
• Volume: 331
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2003.09.005

✦ Synopsis

The Onsager linear relations between macroscopic ows 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 uctuations, represented as the limit of ÿnite-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-deÿnite, 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 ÿnd that this evolution need not be monotonic. The example of an ideal Knundsen gas is considered as an illustration.