In this paper, we generalize the interpretation of the entropy criterion by using stochastic feedback. When a common white Gaussian noise of zero mean and unit variance is applied, the entropy of a transfer function is shown to be equivalent to the maximum variance of the outputs fed back and added to the input through multiplication of a stochastic gain. It turns out that the existing minimum entropy control is useful for minimizing the worst effect of external noises on the outputs when stochastic feedback is applied. (C) 2011 Elsevier Ltd. All rights reserved.