Local equivalence of reversible and general Markov kinetics

We consider continuous-time Markov kinetics with a finite number of states and a positive equilibrium P∗. This class of systems is significantly wider than the systems with detailed balance. Nevertheless, we demonstrate that for an arbitrary probability distribution P and a general system there exists a system with detailed balance and the same equilibrium that has the same velocity dP/dt at point P. The results are extended to nonlinear systems with the generalized mass action law.