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:
“For although memories, of a season, for example,
Melt into a single snapshot, one cannot guard, treasure
That stalled moment. It too is flowing, fleeting;
It is a picture of flowing, scenery, though living, mortal,
Over which an abstract action is laid out in blunt,
Harsh strokes.”
—John Ashbery (b. 1927)
“You do not mean by mystery what a Catholic does. You mean an interesting uncertainty: the uncertainty ceasing interest ceases also.... But a Catholic by mystery means an incomprehensible certainty: without certainty, without formulation there is no interest;... the clearer the formulation the greater the interest.”
—Gerard Manley Hopkins (1844–1889)