Master equations of statistical physics can be described using a pseudo-quantum formalism. This formalism is applied here to operators a and a which satisfy the nonstandard commutation relation of a q-statistics (aa - qa a = 1). In the simplest cases, this leads to a master equation which describes unusual dynamics and equilibrium distributions which are a generalization of Poisson statistics. As a physical realization with a temperature dependent q-factor we discuss the exchange of particles in a pore. There results a phase transition at a critical confinement temperature T c below which complete exchange is impossible.