  Spiking activity from populations of neurons display causal interactions and
memory effects. Therefore, they are expected to show some degree of
irreversibility in time. Motivated by the spike train statistics, in this paper
we build a framework to quantify the degree of irreversibility of any maximum
entropy distribution. Our approach is based on the transfer matrix technique,
which enables us to find an homogeneous irreducible Markov chain that shares
the same maximum entropy measure. We provide relevant examples in the context
of spike train statistics
