The basics of equilibrium statistical mechanics were presented in Chapter 5. In general, most systems of interest in engineering and science are not in equilibrium but are in some nonequilibrium condition. A familiar example of a nonequilibrium state is that of a metal under the application of an applied electric field. An electrical current flows in the metal, resulting in a net transport of charge from one place to another. Such a state is highly unusual; there are relatively few ways in which the system can be arranged so as to provide a specific current flow. Other examples of systems that are in nonequilibrium are systems with a temperature or particle gradient. In these systems, there is a net transport of particles from one part of the system to another in order to establish equilibrium. Hence, in general, nonequilibrium statistical mechanics is concerned with the description of transport phenomena.

How are the states described above different from equilibrium? To answer this question, let us recall the definition of equilibrium from Chapter 5. In the discussion in Chapter 5, it was argued that the most random configuration of a system corresponds to the equilibrium configuration. If we consider a free isolated electron gas, the most random configuration of that gas would be one in which the momentum of the electrons is totally randomized in direction. When the individual values of the momentum are summed over, the net momentum would then be zero, since on average for every electron with a forward-directed momentum, there exists an electron with a compensating negative momentum equal in value.