  Detailed fluctuation theorem, a microscopic version of the steady state
fluctuation theorem, has been proposed by Jarzynski and demonstrated in the
case of Hamiltonian systems weakly coupled with reservoirs. We show that an
identical theorem for phase space compressibility rate can be derived for
systems evolving under non-Hamiltonian extended system dynamics, without
certain limiting assumptions made in the original work. Our derivation is based
on the non-Hamiltonian phase space formulation of statistical mechanics and
does not rely on any assumptions of thermodynamic nature. This version of the
detailed fluctuation theorem is shown to be generic enough to be applicable to
several thermostatting schemes. It is shown that in equilibrium, this detailed
fluctuation theorem boils down to the detailed balance equation and it is
further shown to reproduce the Jarzynski's work theorem for driven systems.
