The statistical and classical thermodynamics framework developed in Chapters 1–8 of this text is based on analysis of systems at equilibrium. In Chapter 9 we explore the extension of this framework to systems that are not in equilibrium. This chapter focuses on systems that exhibit steady spatial variations of properties. Systems of this type are modeled as having local thermodynamic equilibrium and obeying a linear relation between fluxes and affinities. Analysis of microscale features of such linear systems is shown to link correlation moments and kinetic coefficients. The Onsager reciprocity relations are subsequently derived. Thermoelectric effects are examined as an example application of the nonequilibrium linear theory developed in this chapter.

Properties in Nonequilibrium Systems

The thermodynamic theoretical framework developed in previous chapters of this text is limited to analysis of equilibrium states. Often, however, it is the process that takes the system from one state to another that is of primary interest. Overall changes accomplished during the process can be determined by analyzing the initial and final states using equilibrium thermodynamics. If the process is very slow, it may be well approximated by a sequence of equilibrium states, and a quasistatic model may adequately predict the outcome of the process.

In many real processes, the departure from equilibrium is so severe that the quasistatic model is too inaccurate to be useful. The objective of this chapter is to develop thermodynamic tools that can be applied to irreversible processes in nonequilibrium systems.