# Entropy Production

## Entropy Production

the entropy arising in a physical system per unit time as a result of nonequilibrium processes occurring in the system. The entropy production per unit volume is called the local entropy production.

If thermodynamic forces *X _{i}*—such as temperature gradients, concentration gradients of components, gradients of the components’ chemical potentials, gradients of mass velocity, and, in heterogeneous systems, the finite differences of thermodynamic parameters—produce in a system the conjugate fluxes

*J*—for example, fluxes of heat, matter, and momentum—then the local entropy production σ in such a nonequilibrium system is

_{i}where *m* is the number of driving thermodynamic forces. The total entropy production is equal to the integral of σ over the system’s volume. If the thermodynamic fluxes and forces are constant in space, then the total entropy production differs from the local production only by a factor equal to the volume of the system. The relation between the fluxes *J _{i}* and the thermodynamic forces

*x*producing the fluxes is given by the linear equations

_{i}where the *L _{ik}* are the kinetic coefficients (

*see*ONSAGER THEOREM). Consequently, the entropy production is

that is, the entropy production is a quadratic form in the thermodynamic forces.

Entropy production is nonzero and positive for irreversible processes; indeed, the criterion for irreversibility is σ ≠ 0. According to the Prigogine theorem, the entropy production is minimum in stationary states. The specific expression for the kinetic coefficients entering into the entropy production is determined in terms of the interaction potentials of the particles by the methods of nonequilibrium statistical thermodynamics.

D. N. ZUBAREV