It was shown that the principle of the fastest descent in thermodynami
cs of non-equilibrium processes is a physical foundation of progressiv
e evolution of animals and plants. Progressive evolution is related; o
n the one hand, to enhanced bioenergetics, and, on the other one, to i
mprovement of the living system organization (improvement of the syste
m of regulation and control). A curve of bioenergetic progress of anim
als is represented and the rate of bioenergetic progress in different
geological periods has been calculated. We propose that in the type Ve
rtebrata the progressive evolution related to improvement of the proce
sses of regulation and control can be judged according to changes in t
he relative brain size. The. data are provided on changes of the coeff
icient of encephalization in the course of evolution of vertebrates.