Large Negative Numbers in Number Theory, Thermodynamics, Information Theory, and Human Thermodynamics

Russian Journal of Mathematical Physics. 2016. Vol. 23. No. 4. P. 509–524.

Maslov V. P.

We show how the abstract analytic number theory of Maier, Postnikov, and others can be extended to include negative numbers and apply this to thermodynamics, information theory, and human thermodynamics. In particular, we introduce a certain large number N_0 on the "zero level" with a high multiplicity number qi ≫ 1 related to the physical concept of gap in the spectrum. We introduce a general notion of "hole," similar to the Dirac hole in physics, in the theory. We also consider analogs of thermodynamical notions in human thermodynamics, in particular, in connection with the role of the individual in history.

Keywords: Phase transition, the number of degrees of freedom, human thermodynamics, debts, information theory, disinformation, classical number theory,, abstract number theory, the Lagrangian manifold, The Poisson adiabat