Information entropy and temperature of binary Markov chains

We propose two different approaches for introducing the information temperature of binary Nth-order Markov chains. The first approach is based on a comparison of Markov sequences with equilibrium Ising chains at given temperatures. The second approach uses probabilities of finite-length subsequences of symbols occurring, which determine their entropies. The derivative of the entropy with respect to the energy gives the information temperature measured on the scale of introduced energy. For the case of a nearest-neighbor spin-symbol interaction, both approaches give similar results. However, the method based on the correspondence of the N-step Markov and Ising chains appears to be very cumbersome for N > 3. We also introduce the information temperature for the weakly correlated one-parametric Markov chains and present results for the stepwise and power memory functions. An application of the developed method to obtain the information temperature of some literary texts is given.