Field - Theoretical Methods and Nonextensive Systems

The Boltzmann-Gibbs statistical mechanics and the standard thermodynamics are very useful in the discussion of extensive systems. However, they are not good to study situations where nonextensive e ects occur, for instance, systems involving long-range interactions (e. g., d = 3 gravitation)[1, 2], long-range microscopic memory[3], and systems with a relevant (multi)fractal-like structure. On the other hand, the investigations based on the Tsallis entropy[4] mainly focuses on the study of nonextensive problems. Examples of these applications are the L evy superdi usion[5, 6] and anomalous correlated di usion[7], turbulence in a two-dimensional pure electron plasma[8], thermalization of an electron-phonon system[9], astrophysical applications[10], dynamical systems[11, 12], among others[13].