Irreversibility resulting from contact with a heat bath caused by the   finiteness of the system
  When a small dynamical system that is initially in contact with a heat bath is detached from this heat bath and then caused to undergo a quasi-static adiabatic processes, the statistical distribution of the system's energy differs from that of an equilibrium ensemble. Subsequent contact of the system with another heat bath is inevitably irreversible, hence the entire process cannot be reversed without a net energy transfer to the heat baths. 
K. Sato, K. Sekimoto, T. Hondou and F. Takagi