The problem of relaxation to equilibrium

When a thermodynamic system is released from any constraint, after some time its evolution will render it into an equilibrium state. Although the description of this relaxation to thermodynamic equilibrium has been attempted through both classical (Hamilton's equations) or quantum (Schr\"odinger equation) approaches, no success has been achieved without recurring to additional hypotheses. The present work demonstrates the possibility of reaching equilibrium states in a simple classical gaseous system, by imposing non-strict boundary conditions, in the sense that all interactions with the container walls must occur according to Heisenberg's uncertainty principle.