Seminarium KMMF "Teoria Dwoistości"

We discuss the classical theorem of D. Ruelle (1970), later refined by M. Lewin, concerning bounds on correlation functions in classical systems. The theorem states that for systems with superstable and lower-regular pairwise interactions, the correlation functions are uniformly bounded by a constant independent of the system size. Moreover, particle number fluctuations in subsystems are also bounded by constants that do not depend on the total volume of the system. These bounds play a fundamental role in the analysis of the thermodynamic limit and provide useful estimates in classical statistical physics.