Entropy minimization within the maximum entropy approach

A procedure of the minimization of the maximum entropy with respect to an external driving force mu is proposed. In application to coupled dynamic-stochastic systems such an approach allows one to reduce the uncertainty in estimating the dynamic counterpart (a probe or a model) parameters. In its turn this permits to estimate an optimal driving path giving a maximal information on the probability distribution f(x vertical bar mu) of the stochastic counterpart with a given probe/model theta(mu vertical bar x). It is found that the functional form of the model should be similar to the observed/measured one theta(mu), while the minimum uncertainty is reached when the distribution becomes independent of the driving mu.