The ambiguous meaning of irreversibility

Irreversibility of spontaneous macroscopic dynamics and its asymmetry with respect to the sign reversal of the variable $t$ is usually interpreted as a genuine property of complex isolated systems. Discussion of the kinetics involved in Joule’s experiment concerning spontaneous expansion of a gas shows that the isolation hypothesis results from ambiguous definitions of a number of keywords. Whereas Poincar'{e}'s apparent irreversibility result from conservative Hamiltonian dynamics, full relaxation implies interaction with the outside world. Only the latter process leads to entropy change.