The minimal temperature of Quantum Refrigerators

A first principle reciprocating quantum refrigerator is investigated with the purpose of determining the limitations of cooling to absolute zero. We find that if the energy spectrum of the working medium possesses an uncontrollable gap, then there is a minimum achievable temperature above zero. The reason is that such a gap, combined with a negligible amount of noise, prevents adiabatic following during the expansion stage which is necessary condition for reaching T_c --> 0.