  The nature takes the easiest and most accessible paths and, hence, processes
are accomplished very quickly in a minimum time. In 1662 P. Fermat used this
principle to work out the refraction law. This was one of the first known
attempts at successful deductive description of a physical phenomenon involving
the variational principle. Presently researchers concerned with nonequilibrium
processes have turned back to Fermat's idea in the form of the maximum entropy
production principle (MEPP). MEPP has proved to be good for understanding and
description of diverse nonequilibrium processes in physics, chemistry and
biology. This brings up two questions: 1) Can this principle claim to be the
basis of all nonequilibrium physics? 2) Is it possible to prove MEPP?
