  The Liouville Equation, the starting point of non-relativistic,
non-equilibrium classical statistical mechanics, is problematic in special
relativity because of two problems. A relativistic Hamiltonian is claimed not
to exist for interacting particles and the problem of what time to use since
the particles will all have their own time as part of their space-time
coordinate. In this paper, I look at this problem and surprisingly found that
there is no special relativistic Liouville equation in 8N phase space, where N
is the number of particles, because the canonical Hamiltonian is zero for both
non-interacting and interacting particles. This is due to the parametrization
symmetry in defining a single time for the Liouville equation evolution, which
results in a constraint.This is similar to the fact that in general relativity,
diffeomorphism invariance of the theory always give a zero Hamiltonian because
of a constraint.

Statistical Mechanics;High Energy Physics - Theory