Tsallis maximum entropy principle and the law of large numbers

Tsallis has suggested a nonextensive generalization of the Boltzmann-Gibbs entropy, the maximization of which gives a generalized canonical distribution under special constraints. In this Brief Report, we show that the generalized canonical distribution so obtained may differ from that predicted by the law of large numbers when empirical samples are held to the same constraint. This conclusion is based on a result regarding the large deviation property of conditional measures and is confirmed by numerical evidence.