Information temperature as a parameter of random sequence complexity

TL;DR

This paper introduces the concept of information temperature as a novel parameter to quantify the complexity of random sequences, especially in high-order Markov chains, and explores its potential as an indicator of text-generating intelligence.

Contribution

It proposes a new method to define sequence complexity using information temperature and analyzes its relation to sequence memory depth and complexity.

Findings

Maximum complexity occurs at high information heat capacity.

Information temperature correlates with sequence memory depth.

Potential application as an indicator of text-generating agent intelligence.

Abstract

In this study, we continue our exploration of the concept of information temperature as a characteristic of random sequences. We describe methods for introducing the information temperature in the context of binary high-order Markov chain with step-wise memory and investigate the application of the temperature as a parameter of the sequence complexity. We aim to define complexity based on the derivative of entropy with respect to information temperature, drawing an analogy to thermodynamic heat capacity. The maximum complexity of a random sequence is achieved when its information "heat capacity" approaches its highest possible value, which is directly influenced by the sequence memory depth. We also discuss the potential of utilizing information temperature as an indicator of the intellectual level exhibited by any text-generating agent.