This text investigates systems of an infinite number of particles, in particular, the justification of the procedure of thermodynamic limit transition. This is the first detailed study of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. The authors' updates in this edition reflect developments in theory over the last ten years. The authors also simplified certain sections, presenting them more systematically and add new references. The book is useful to postgraduate students and researchers in theoretical physics and mathematics.
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