Abstract Formulation
Let denote fluctuations from equilibrium values in several thermodynamic quantities, and let be the entropy. Then, Boltzmann's entropy formula gives for the probability distribution function, A=const. Assuming the fluctuations are small, the probability distribution function can be expressed through the second differential of the entropy
where we are using Einstein summation convention and is a positive definite symmetric matrix.
Using the quasi-stationary equilibrium approximation, that is, Assuming that the system is only slightly non-equilibrium, we have
Suppose we define thermodynamic conjugate quantities as, which can also be expressed as linear functions (for small fluctuations):
Thus, we can write where are called kinetic coefficients
The principle of symmetry of kinetic coefficients or the Onsager's principle states that is a symmetric matrix, that is
Read more about this topic: Onsager Reciprocal Relations
Famous quotes containing the words abstract and/or formulation:
“Delight at having understood a very abstract and obscure system leads most people to believe in the truth of what it demonstrates.”
—G.C. (Georg Christoph)
“Art is an experience, not the formulation of a problem.”
—Lindsay Anderson (b. 1923)