Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts

TL;DR

This paper introduces a novel probability theory aligned with modern thermodynamics, incorporating fuzzy sets and measurement effects, leading to new models in physics and economics, including debt crisis analysis.

Contribution

It develops a new probability framework compatible with thermodynamics and applies it to economics, offering insights into debt crises and correcting classical economic laws.

Findings

Introduction of a one-parameter family of ideal gases.

New approach to probability including a revised notion of independence.

Application to economic theory and debt crisis modeling.

Abstract

We show that G\"odel'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 fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases. In turn, this leads to a new approach to probability theory (including the new notion of independent events). As applied to economics, this gives the correction, based on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us to consider the theory of debt crisis.