Kelly and Leff demonstrated and discussed formal and conceptual similarities between basic thermodynamic formulas for the classical ideal gas and black body photon gas. Leff pointed out that thermodynamic formulas for the photon gas cannot be deduced
completely by thermodynamic methods since these formulas hold two characteristic parameters, {it r} and {it b}, whose accurate values can be obtained exclusively by accurate methods of the quantum statistics (by explicit use of the Plancks or Bose-Einstein distribution). In this work we prove that the complete quantum thermodynamics of the black body photon gas can be done by simple, thermodynamic (non-statistical) methods. We prove that both mentioned parameters and corresponding variables (photons number and pressure) can be obtained very simply and practically exactly (with relative error about few percent), by non-statistical (without any use of the Plancks or Bose-Einstein distribution), quantum thermodynamic methods. Corner-stone of these methods represents a quantum thermodynamic stability condition that is, in some degree, very similar to quantum stability condition in the Bohr quantum atomic theory (de Broglies interpretation of the Bohr quantization postulate). Finally, we discuss conceptual similarities between black body photon gas entropy and Bekenstein-Hawking black hole entropy.
In this work we consider some consequences of the Bohr-Sommerfeld-Hansson (Old or quasi-classical) quantum theory of the Newtonian gravity, i.e. of the gravitational atom. We prove that in this case (for gravitational central force and quantized angu
lar momentum) centrifugal acceleration becomes formally-theoretically dependent (proportional to fourth degree) of the mass of gravitational electron rotating around gravitational nucleus for any quantum number (state). It seemingly leads toward a paradoxical breaking of the relativistic equivalence principle which contradicts to real experimental data. We demonstrate that this equivalence principle breaking does not really appear in the (quasi classical) quantum theory, but that it necessary appears only in a hypothetical extension of the quantum theory that needs a classical like interpretation of the Bohr-Sommerfeld angular momentum quantization postulate. It is, in some sense, similar to Bell-Aspect analysis that points out that a hypothetical deterministic extension of the quantum mechanics, in distinction to usual quantum mechanics, can reproduce experimental data if and only if it is non-local (superluminal) in contradiction with relativistic locality (luminality) principle.
In this work we suggest a simple theoretical solution of the Mpemba effect in full agreement with known experimental data. This solution follows simply as an especial approximation (linearization) of the usual heat (transfer) equation, precisely line
arization of the second derivation of the space part of the temperature function (as it is well-known Newton cooling law can be considered as the effective approximation of the heat (transfer) equation for constant space part of the temperature function).
