Information temperature as a parameter of random sequence complexity

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.