Towards the unified non-classical physics: Account for quantum fluctuations in equilibrium thermodynamics via the effective temperature

The concept of effective temperature (ET) T* (T0, T) is used in order to approximately "quantize" the thermodynamic functions of the dynamical object which is in the thermal equilibrium with thermal bath being at constant temperature T (T0 = E0/kB, where E0 is the ground-state energy, kB - Boltzmann constant, is the characteristic "quantum" temperature of the system itself). On these grounds the extensive comparative investigation is carried out for the "standard model" of statistical mechanics - the one-dimensional harmonic oscillator (HO). Three well-known approaches are considered and their thermodynamic consequences thoroughly studied. These are: the exact quantum, or non-classical Planck-Einstein approach, intermediate, or semiclassical Bloch-Wigner approach and, finally, the pure classical, or Maxwell-Boltzmann approach. © Yu.G. Rudoy, A.D. Sukhanov.