For bosons and fermions a new representation of the Hamilton operator corresponding to creation and annihilation of clusters is given. The obtained principle of correspondence between symbols and operators allows us to quantize the entropy and free energy. The minimal value of the quantum free energy in the thermodynamical limit matches the classical free energy. An estimate of this minimal value for a boson system with strong interaction, where the phase transition to superfluidity is possible, is presented.
Department of Quantum Statistics and Field Theory, Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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