Truly isolated physical systems do not exist in reality (except for the universe as a whole), because, for example, there is always gravity between a system with mass and masses elsewhere. However, real systems may behave nearly as an isolated system for finite (possibly very long) times. The concept of an isolated system can serve as a useful model approximating many real-world situations. It is an acceptable idealization used in constructing mathematical models of certain natural phenomena; e.g., the Sun and planets in our solar system, and the proton and electron in a hydrogen atom are often treated as isolated systems. But from time to time, a hydrogen atom will interact with electromagnetic radiation and go to an excited state.
In the attempt to justify the postulate of entropy increase in the second law of thermodynamics, Boltzmann’s H-theorem used equations which assumed a system (e.g., a gas) was isolated: i.e., that all the mechanical degrees of freedom could be specified, treating the walls simply as mirror boundary conditions. This inevitably lead to Loschmidt's paradox. However, if the stochastic behavior of the molecules in actual walls is considered, along with the randomizing effect of the ambient, background thermal radiation, Boltzmann’s assumption of molecular chaos can be justified.