Eventological H-theorem

TL;DR

This paper introduces the eventological H-theorem, providing a mathematical foundation for the second law of eventology, which justifies the use of Gibbs-like distributions to model rational decision-making processes.

Contribution

It establishes the eventological H-theorem as a counterpart to the Boltzmann H-theorem, supporting the application of entropy-minimizing distributions in eventology.

Findings

Proves the eventological H-theorem.

Justifies Gibbs and anti-Gibbs distributions in eventology.

Provides a mathematical basis for the second law of eventology.

Abstract

We prove the eventological $H$-theorem that complements the Boltzmann H-theorem from statistical mechanics and serves as a mathematical excuse (mathematically no less convincing than the Boltzmann H-theorem for the second law of thermodynamics) for what can be called "the second law of eventology", which justifies the application of Gibbs and "anti-Gibbs" distributions of sets of events minimizing relative entropy, as statistical models of the behavior of a rational subject, striving for an equilibrium eventological choice between perception and activity in various spheres of her/his co-being.