It is well known that any irreducible and aperiodic Markov chain has exactly one stationary distribution, and for any arbitrary initial distribution, the sequence of distributions at time n converges to the stationary distribution, that is, the Markov chain is approaching equilibrium as n→∞. In this paper, a characterization of the aperiodicity in existential terms of some state is given. At the same time, a P system with external output is associated with any irreducible Markov chain. The designed system provides the aperiodicity of that Markov chain and spends a polynomial amount of resources with respect to the size of the input. A comparative analysis with respect to another known solution is described.