Mutual information of population codes and distance measures in probability space

We studied the mutual information between a stimulus and a system consistin g of stochastic, statistically independent elements that respond to a stimu lus. Using statistical mechanical methods the properties of the mutual info rmation (MI) in the limit of a large system size N are calculated. For cont inuous valued stimuli, the MI increases logarithmically with N and is relat ed to the log of the Fisher information of the system. For discrete stimuli the MI saturates exponentially with N. We find that the exponent of satura tion of the MI is the Chernoff distance between response probabilities that are induced by different stimuli.