Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

Experimental recordings of the collective activity of interacting spiking neurons exhibit 1 random behavior and memory effects, thus the stochastic process modeling the spiking activity 2 is expected to show some degree of time irreversibility. We use the thermodynamic formalism to 3 build a framework, in the context of spike train statistics, to quantify the degree of irreversibility 4 of any parametric maximum entropy measure under arbitrary constraints, and provide an explicit 5 formula for the information entropy production of the inferred Markov maximum entropy process. 6 We provide examples to illustrate our results and discuss the importance of time irreversibility for 7 modeling the spike train statistics. 8