Nonequilibrium Thermodynamics

NONEQUILIBRIUM THERMODYNAMICS

Postulate I (Existence of thermodynamic functions)

For a system in which irreversible processes are taking place, all thermodynamic functions of state exist for each element of the system. These thermodynamic quantities for the nonequilibrium system are the same functions of the local state variables as the corresponding equilibrium thermodynamic quantities.

Postulate II (Phenomenological equations)

The fluxes or currents Ji are linear, homogeneous functions of the forces Xi ’

J ii= ∑ LXjj (1) j

Where Lij the phenomenological coefficients, are independent of the forces.

Postulate III (Onsager reciprocal relations)

Provide a proper choice is made for fluxes Ji and forces Xi ’ the matrix of phenomenological coefficients Lij is symmetric.

Lij= L ji (2)

“proper choice”

TJσ = ∑ iiX (3) i

If a set of fluxes and forces satisfies the equations (1), (2) and (3), then this is a proper choice.

Conjugated Fluxes and Forces

In Eq. (3) Ji and Xi are conjugated. (Same index i)

There are many possible sets of conjugated fluxes and forces for a given system, but Eq. (2) may or may not hold for a particular choice of a set.

The study of an irreversible process of arbitrary complexity consists in finding

(i) the conjugated fluxes and forces Ji and Xi from Eq. (3) by calculating the rate of entropy production.

(ii) The study of the phenomenological equations (1) and the Onsager relations (2).

conjugated phenomena

cross phenomena

In general, if we write the linear relations, Eq. (1), for a set of conjugated fluxes and forces, the phenomenological coefficients so defined may or may not obey Eq. (2).

The following transformations are of interest:

(A) Fluxes and Forces Fluxes and Forces satisfying Eqs. satisfying Eqs. (1), (2), (3) (1), (3), not (2)

(B) Fluxes and Forces Fluxes and Forces satisfying Eqs. satisfying Eqs. (1), (3), not (2) (1), (2), (3)