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We consider a stochastic process which is (a) described by a continuous-timeMarkov chain on only short time-scales and (b) constrained to conserve a numberof hidden quantities on long time-scales. We assume that the transition matrixof the Markov chain is given and the conserved quantities are known to exist,but not explicitly given. To study the stochastic dynamics we propose to usethe principle of stationary entropy production. Then the problem can betransformed into a variational problem for a suitably defined action and withtime-dependent Lagrange multipliers. We show that the stochastic dynamics canbe described by a Schrodinger equation, with Lagrange multipliers playing therole of phases, whenever (a) the transition matrix is symmetric or the detailedbalance condition is satisfied, (b) the system is not too far from theequilibrium and (c) the number of the conserved quantities is large.

Entropic Mechanics: towards a stochastic description of quantum mechanics