Modern understanding of non-equilibrium processes in distributed systems based on experimental data, obtained with use of high-precision instruments, is fundamentally different from the previously common opinion that non-equilibrium processes are irreversible non-stationary processes that can be described by partial differential equations. Attempts to apply conventional mathematical models of continuum mechanics far from thermodynamic equilibrium led to serious errors. The main problem is that all physical concepts are related to the system states near local equilibrium and a generalization of one concept implies the revision of all fundamentals of thermodynamics. In order to avoid contradictions, understanding of special features characterizing the system response to an external perturbation out of equilibrium is needed for mathematical modeling.
In this chapter, we list and briefly describe those features that distinguish dynamic processes far from local equilibrium from quasi-static near-equilibrium processes. The influence of each of these non-equilibrium effects will be considered separately and the information currently available to describe it is given.