Algorithmic entropy, thermodynamics, and game interpretation

TL;DR

This paper introduces a new extremal problem to derive relations for mean length and algorithmic entropy, framing them as players in a game inspired by thermodynamic concepts in quantum and classical contexts.

Contribution

It presents a novel extremal problem approach to relate mean length and algorithmic entropy, and interprets these as players in a thermodynamic-inspired game.

Findings

Derived basic relations for mean length and entropy.

Presented a new extremal problem for these relations.

Proposed a game interpretation of length and entropy.

Abstract

Basic relations for the mean length and algorithmic entropy are obtained by solving a new extremal problem. Using this extremal problem, they are obtained in a most simple and general way. The length and entropy are considered as two players of a new type of a game, in which we follow the scheme of our previous work on thermodynamic characteristics in quantum and classical approaches.