  In terms of the stochastic process of quantum-mechanical version of Markov
chain Monte Carlo method (the MCMC), we analytically derive macroscopically
deterministic flow equations of order parameters such as spontaneous
magnetization in infinite-range ($d(=\infty)$-dimensional) quantum spin
systems. By means of the Trotter decomposition, we consider the transition
probability of Glauber-type dynamics of microscopic states for the
corresponding $(d+1)$-dimensional classical system. Under the static
approximation, differential equations with respect to macroscopic order
parameters are explicitly obtained from the master equation that describes the
microscopic-law. In the steady state, we show that the equations are identical
to the saddle point equations for the equilibrium state of the same system. The
equation for the dynamical Ising model is recovered in the classical limit. We
also check the validity of the static approximation by making use of computer
simulations for finite size systems and discuss several possible extensions of
our approach to disordered spin systems for statistical-mechanical informatics.
Especially, we shall use our procedure to evaluate the decoding process of
Bayesian image restoration. With the assistance of the concept of dynamical
replica theory (the DRT), we derive the zero-temperature flow equation of image
restoration measure showing some `non-monotonic' behaviour in its time
evolution.
