  We rigorously show that the probability to have a specific trajectory of an
externally perturbed classical open system satisfies a universal symmetry for
Liouvillian reversible dynamics. It connects the ratio between the
probabilities of time forward and reversed trajectories to a degree of the time
reversal asymmetry of the final phase space distribution. Indeed, if the final
state is in equilibrium, then the forward and reversed net transition
probabilities are equal, which gives a generalization of the detailed balance
principle. On the other hand, when the external forcing maintains the system
out of equilibrium, it expresses an asymmetry for the probabilities of the time
forward and reversed trajectories. Especially, it gives a microscopic
expression of the heat flowing to a system from a reservoir where the
subdynamics seems like a Markovian stochastic process.
  Also, it turns out that the expression of the microscopic reversibility holds
both for the conservative and dissipative dynamics with an arbitrary initial
state and external forcing.
