Local equivalence of reversible and general Markov kinetics

► We study the classes of Markov chains with a given equilibrium distribution. ► We compare the general Markov chains and the reversible chains with detailed balance. ► For any general chain there is a reversible chain with the same velocity at a given point. ► The classes of general and reversible chains locally coincide. ► They have the same cone of possible velocities at every non-equilibrium distribution.