| Contents |
| Typical examples of Markov operators are solution operators
to linear PDEs of second order, describing the evolution of probability
densities for classical particles.
A general mathematical framework,
applicable for general classical physical systems,
can be developed to describe such equations
and many others in a unique setting. This allows to understand better the
underlying structure of such equations. In this setting,
Markov operators provide some general inequalities defining a natural order.
This order is well known as
order in majorization theory in linear algebra or order of
rearrangement of functions in integration theory.
In addition, the inequalities show the irreversibility of time for both
forward as well as backward running time, depending on the
physical meaning of the variables in the underlying equations. |
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