We consider a spike-generating stationary Markov process whose transition probabilities are known. We show that there is a canonicalpotential whose Gibbs distribution, obtained from the MaximumEntropy Principle (MaxEnt), is the equilibrium distribution of thisprocess. We provide a method to compute explicitly and exactly thispotential as a linear combination of spatio-temporal interactions.The method is based on the Hammersley Clifford decomposition andon periodic orbits sampling. An explicit correspondence between theparameters of MaxEnt model and the parameters of Markovianmodels like the Generalized-Linear Model can be established. Wealso provide numerical results.