  Starting from an algebraic approach of quantum physics it has been shown via
the Tomita-Takesaki theorem and the KMS condition that the canonical density
matrix contains the dynamics of the system provided we use a rescaling of time.
In this paper we show that the path integral form of the partition function
reveals a dynamics which is complementary of the one given by the
Tomita-Takesaki theorem. To do that we work in the spirit of a
Feynman'conjecture. We define the entropy as a measure of the disorder in space
time. By using an equilibrium condition we introduce a natural time scale that
it is precisely the one appearing in the Tomita-Takesaki theorem. For this time
scale depending on the temperature but not on the system properties our
definition of entropy is identical to the thermodynamic one. The underlying
dynamics associated with the partition function allows us to derive a
$\bf{H}$-$theorem$. It is obtained in the thermodynamic limit and provided we
are in a regime in which the thermal fluctuations are larger than the quantum
ones.
