Small systems: when does thermodynamics apply?

The validity of using temperature to describe quantitatively the state of excitation of an isolated nucleus is examined. The problem arises because of the small number of particles in a nucleus. As a consequence, it is possible to construct a heat bath and so fix the temperature. Another definition is used that leads to an uncertainty in the measured temperature which tends to zero as the number of particles in the system increases. The emphasis is on the nuclear problem but it is presumed that similar considerations apply to other small isolated systems such as single molecules, atomic clusters containing two to several hundred atoms, helium droplets, etc