  We consider continuous--time Markov kinetics with a finite number of states
and a given positive equilibrium distribution P*. For an arbitrary probability
distribution $P$ we study the possible right hand sides, dP/dt, of the
Kolmogorov (master) equations. We describe the cone of possible values of the
velocity, dP/dt, as a function of P and P*. We prove that, surprisingly, these
cones coincide for the class of all Markov processes with equilibrium P* and
for the reversible Markov processes with detailed balance at this equilibrium.
Therefore, 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 set of Lyapunov functions for the
reversible Markov processes coincides with the set of Lyapunov functions for
general Markov kinetics. The results are extended to nonlinear systems with the
generalized mass action law.
