Abstract: From the mathematical point of view, information sources can be 1-to-1 mapped to stochastic processes. Known from the theory of chaos, multi-fractal of stochastic process is a key characteristic of its dynamics, of which entropy rate is a special fractal dimension named information dimension. The paper introduces methods of statistical physics to compute the multi-fractal of stochastic process so that the entropy rate of source can be obtained at once. Take binary hidden Markov processes as example, the paper demonstrate how this approach works. The results shows that the methods is applicable to numerically approximate the entropy rate of binary hidden Markov processes (BHMPs) in practical applications, and it can be applied in more generalized kinds of information sources.