In optimization problems, the contribution of a variable to fitness often depends on the states of other variables. This phenomenon is referred to as epistasis or linkage. In this paper, we show that a new theory of epistasis can be established on the basis of Shannon's information theory. From this, we derive a new epistasis measure called entropic epistasis and some theoretical results. We also provide experimental results verifying the measure and showing how it can be used for designing efficient evolutionary algorithms.