Chaos from nonlinear Markov processes: Why the whole is different from the sum of its parts

Abstract

Nonlinear Markov processes have been frequently used to address bifurcations and multistability in equilibrium and non-equilibrium many-body systems. However, our understanding of the range of phenomena produced by nonlinear Markov processes is still in its infancy. We demonstrate that in addition to bifurcations and multistability nonlinear Markov processes can exhibit another key phenomena well known in the realm of nonlinear physics: chaos. It is argued that chaotically evolving process probabilities are a generic feature of many-body systems exhibiting nonlinear Markov processes even if the isolated subsystems do not exhibit chaos. That is, when considering a nonlinear Markov process as an entity of its own type, then the nonlinear Markov process in general is qualitatively different from its constituent subprocesses, which reflects that the many-body system as a whole is different from the sum of its parts.