Towards a large deviation theory for strongly correlated systems

A large-deviation connection of statistical mechanics is provided by N independent binary variables, the (N → ∞) limit yielding Gaussian distributions. The probability of n ̸= N/2 out of N throws is governed by e−Nr , r related to the entropy. Large deviations for a strong correlated model characterized by indices (Q, γ ) are studied, the (N → ∞) limit yielding Q -Gaussians (Q → 1 recovers a Gaussian). Its large deviations are governed by e−Nrq q (∝ 1/N1/(q−1), q > 1), q= (Q− 1)/(γ [3− Q ]) + 1. opens the door towards a large-deviation foundation of nonextensive statistical mechanics.

2012