Description: We consider renewal stochastic processes generated by non-independent events from the perspective that their basic distribution and associated generating functions obey the statistical-mechanical structure of systems with interacting degrees of freedom. Based on this fact we look briefly into the less known case of processes that display phase transitions along time. When the density distribution psi_{n}(t) for the occurrence of the n-th event at time t is considered to be a partition function, of a 'microcanonical' type for n 'degrees of freedom' at fixed 'energy' t, one obtains a set of four partition functions of which that for the generating function variable z and Laplace transform variable epsilon, conjugate to n and t, respectively, plays a central role. *** Journal reference: Physical Review E 83, 031103 (2011)***