On a naive construction of kinetic equation

Abstract

We return to the subject of stability of infinite time asymptotics of kinetic equations. We found a model which is simpler than those studied previously and which shows unstable behavior corresponding to our arguments to appear elsewhere, where, however, a relatively complicated problem was treated. Our simplification to four levels interacting with surroundings enable us to proceed easily through all the way with just a pen and paper. We provide no numerical modelling whose justification causes naturally difficulties to the reader. We draw also further consequences of the found instability, not only with respect to higher order terms in kinetic equations but also concerning the very philosophy of physical modelling. The latter point can give more practically oriented physicist even better motivation than mere speculations about potential instabilities due to higher order terms in perturbation treatments without concrete resolution of correct asymptotics.