Small systems: When does thermodynamics apply

In this paper the validity of the use of temperature to quantitatively describe the state of excitation is an isolated nucleus is examined. The problem arises because of the small number of particles in a nucleus. As a consequence, one cannot construct a ''heat bath'' and so fix the temperature. One must employ another definition which will be described below. It leads as we shall see to an uncertainty in the measured temperature which tends to zero as the number of particles in the system increases. The emphasis will be on the nuclear problem but presumably similar considerations apply to other small isolated systems such as single molecules, atomic clusters containing two to several hundred atoms, helium droplets, etc. The temperature was introduced into nuclear physics some 50 years ago and to describe a nuclear reaction in which a compound system, a highly excited nucleus is formed. Under the assumption that there is an equilibration of the degrees of freedom of the system the probability (and therefore the cross section) for the emission of a neutron of energy ε will be proportional to the density of states rho of the residual nucleus at the energy E/sub 0/ - E/sub 0/ = total energy of the system)