Derivation of the Onsager Principle from Large Deviation Theory
| Autor: | Brian R. La Cour, William C. Schieve |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Statistical Mechanics (cond-mat.stat-mech) Mathematical analysis FOS: Physical sciences Monotonic function Condensed Matter Physics Conditional expectation Microstate (statistical mechanics) Equating Large deviations theory Onsager reciprocal relations Statistical physics Entropy (arrow of time) Rate function Condensed Matter - Statistical Mechanics Mathematics |
| Popis: | 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. 25 pages, 3 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|