  The interrelationship between energy and probability conservation is explored
from the point of view of statistical physics and non-relativistic quantum
mechanics. The simultaneous validity of the law of conservation of energy and
the continuity equation (probability conservation) breaks for an interacting
dynamical system. A separate and independent description of a physical system
can be obtained by requiring that the law of conservation of probability is at
the heart of the derivation of the ''equations of motion''. In effect, The
Schrodinger equation can be viewed as an appropriate factorization of the
continuity equation instead of an energy conservation relation per se.
