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

Abstract

We show that Gödel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of soft sets and of the effect of a measuring device on the experiment.

Analysis of the particle transfer between two systems under unification

“…In the system with lower dimension α, temperature T is higher. Temperature of the united system either equals the arithmetic mean of the temperatures of initial systems (case (1), see (16)) or is lower than this mean value (in case (2), see (23)).…”

“…which defines deviation of the final temperature (turnover rate) from the arithmetic mean of the initial temperatures. Inequalities ( 14) thus hold both in case (1) and in case (2). Final temperature of the united system is thus lower than the arithmetic mean temperature of systems 1 and 2.…”

Demonstrations in mathematics and physics

“…In the paper [10], the case of μ − O( 1 log N ) was calculated. However, if μ > δ, where δ > 0 does not depend on N , then the second integral in formula (11) can be neglected.…”

“…Moreover, the formulas (5)-(10) in [10], which we obtain from number theory, need not be multiplied by the volume V in general. They can be multiplied by V α or, when viewed in a dimensionless form, by (V/V 0 ) α , where α depends on γ only and is preserved for T T c .…”

“…Some time ago I received a negative referee's report from a referee physicist to my paper "The mathematical concept of "phenomenological" equilibrium thermodynamics," which is a version of [9] (elaborated for physicists) overlapping with [10].…”