  A new generic dynamical phenomenon of pseudochaos and its relevance to the
statistical physics both modern as well as traditional one are considered and
explained in some detail. The pseudochaos is defined as a statistical behavior
of the dynamical system with discrete energy and/or frequency spectrum. In
turn, the statistical behavior is understood as time-reversible but
nonrecurrent relaxation to some steady state, at average, superimposed with
irregular fluctuations. The main attention is payed to the most important and
universal example of pseudochaos, the so-called quantum chaos that is dynamical
chaos in bounded mesoscopic quantum systems. The quantum chaos as a mechanism
for implementation of the fundamental correspondence principle is also
discussed.
  The quantum relaxation localization, a peculiar characteristic implication of
pseudochaos, is reviewed in both time-dependent and conservative systems with
special emphasis on the dynamical decoherence of quantum chaotic states. Recent
results on the peculiar global structure of the energy shell, the Green
function spectra and the eigenfunctions, both localized and ergodic, in a
generic conservative quantum system are presented.
  Examples of pseudochaos in classical systems are given including linear
oscillator and waves, digital computer and completely integrable systems. A
far-reaching similarity between the dynamics of a few-freedom quantum system at
high energy levels (n >> 1) and that of many--freedom one (N >> 1) is also
discussed.
