Onsager-Casimir relations revisited
The authors study the fate of the Onsager-Casimir reciprocity relations for a continuous system when some of its variables are eliminated adiabatically. Just as for discrete systems, deviations appear in correction terms to the reduced evolution equation that are of higher order in the time scale ratio. The deviations are not removed by including correction terms to the coarse-grained thermodynamic potential. However, via a reformulation of the theory, in which the central role of the thermodynamic potential is taken over by an associated Lagrangian-type expression, they arrive at a modified form of the Onsager-Casimir relations that survives the adiabatic elimination procedure. There is a simple relation between the time evolution of the redefined thermodynamic forces and that of the basic thermodynamic variables; this relation also survives the adiabatic elimination. The formalism is illustrated by explicit calculations for the Klein-Kramers equation, which describes the phase space distribution of Brownian particles, and for the corrected Smoluchowski equation derived from it by adiabatic elimination of the velocity variable. The symmetry relation for the latter leads to a simple proof that the reality of the eigenvalues of the simple Smoluchowski equation is not destroyed by the addition of higher order corrections, at least not within the framework of a formal perturbation expansion in the time scale ratio.
- Research Organization:
- Johannes Kepler Universitaet Linz, Austria
- OSTI ID:
- 5832453
- Journal Information:
- J. Stat. Phys.; (United States), Vol. 49:1-2
- Country of Publication:
- United States
- Language:
- English
Similar Records
Brownian motion on a manifold
On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
Related Subjects
GENERAL PHYSICS
PARTICLE MODELS
CASIMIR OPERATORS
ONSAGER RELATIONS
STATISTICAL MECHANICS
ADIABATIC PROCESSES
BROWNIAN MOVEMENT
CHAPMAN-ENSKOG THEORY
DISTRIBUTION FUNCTIONS
HERMITIAN OPERATORS
KRAMERS THEOREM
PARTICLE KINEMATICS
PHASE SPACE
QUANTUM MECHANICS
SYMMETRY BREAKING
SYMMETRY GROUPS
THERMODYNAMICS
FUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
SPACE
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics