(A, k)-Dynamics as some generalization of equilibrium quantum statistical mechanics

We show that the quantum statistical mechanics (QSM) describing quantum and thermal properties of objects has only the sense of a particular semiclassical approximation. We propose a more general (than QSM) micro description of objects in a heat bath taken into account a vacuum as an object environment; we call it (A , k)-dynamics (A kD). We construct a new model of thermostat, namely, a quantum heat bath and study its properties including the cases of a "cold" and "thermal" vacua. We introduce a new generative operator, Schroedingerian, or stochastic action operator, and show its fundamental role in the determination such macro-quantities as internal energy, effective temperature, and effective entropy. We establish that in A kD the ratio of effective action to effective entropy at zero temperature equals the universal constant A /2k. This result corresponds to experimental data taken recently under studying of a new matter state-nearly perfect fluid.