  We introduce the notion of an extended moment in time, the duron. This is a
region of temporal ambiguity which arises naturally in the nature of process
which we take to be basic. We introduce an algebra of process and show how it
is related to, but different from, the monoidal category introduced by Abramsky
and Coecke. By considering the limit as the duration of the moment approaches
the infinitesimal, we obtain a pair of dynamical equations, one expressed in
terms of a commutator and the other which is expressed in terms of an
anti-commutator. These two coupled real equations are equivalent to the
Schr\"odinger equation and its dual.
  We then construct a bi-algebra, which allows us to make contact with the
thermal quantum field theory introduced by Umezawa. This allows us to link
quantum mechanics with thermodynamics. This approach leads to two types of
time, one is Schr\"odinger time, the other is an irreversible time that can be
associated with a movement between inequivalent vacuum states. Finally we
discuss the relation between our process algebra and the thermodynamic origin
of time.
