Stochastic processes describe systems in which one or more variables fluctuate randomly. In the first part of the talk, I reviewed basic concepts in stochastic processes and how to express them in terms of localized spin operators and the probability vector (PV). This framework is convenient to compute statistics away from meanfield approximations because it can borrow methods traditionally used in many-body problems in Physics. The second part of the talk addressed the equation for the squared norm of the PV and its correspondence with the Rényi entropy. The general idea and challenges of employing estimates of the Rényi entropy were discussed shortly after. As a practical biological application, I explained the dynamical equations for averages and fluctuations in a simple stochastic epidemic model, highlighting the effects of noise and correlations in heterogeneous finite systems.