Closed system

An Isolated system, is a physical system that does not interact with its surroundings. It obeys a number of conservation laws: its total energy and mass stay constant. They cannot enter or exit, but can only move around inside. An example is in the study of spacetime, where it is assumed that asymptotically flat spacetimes exist.

Truly isolated physical systems do not exist in reality, but real systems may behave nearly this way 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.

Another reason no system can be truly isolated is that even in interstellar space, there is the 2.7 K background blackbody radiation left over from the Big Bang. This heat permeates every physical body in the Universe.

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.

Closed system
By contrast, a closed (but not isolated) system can exchange heat and work, but not matter, with its surroundings. This is a basic concept in thermodynamics, where it is assumed that a thermally isolated (insulated) system can be realized. It is a useful idealization, even if it can only be asymptotically approximated.