New probability theory compatible with the new conception of modern thermodynamics. Economics and crisis of debts (Q455607)

The paper in major parts is a scientific essay on various aspects of the partitio numerorum problem according to Erdős and statistical distributions of relevant partitions, with applications to thermodynamical (statistical ) equilibrium distributions. The author addresses non-standard interpretations of what should be considered a physical macro-state in equilibrium thermodynamics. By turning over to a sand-pile paradox, a discussion follows of the need to replace the Boltzmann distribution by another one, inferred by introducing a system of fuzzy subsets of \(N\) elements (\(N\) being large). An example of the Bose-Einstein distribution is analyzed that way. The paper refers to a multitude of previous works by the present author and in fact can hardly be understood without referring to the explicit source material. A number of terms with a well-established meaning in the physics literature is used in the paper in a non-standard vein. Examples pertain to a fractional dimension in number theory which is not related to the standard fractal one, Bohr's complementarity principle, the concept of Wiener quantization. The economic part is extremely concise and a justification of its Bohr complementarity input is far from being obvious.