Suppose that by a suitable external mechanical or electrical arrangement one can add to the energy of the heat reservoir whenever the reservoir passes

Suppose that by a suitable external mechanical or electrical arrangement one can add αε to the energy of the heat reservoir whenever the reservoir passes to the system the quantum of energy e. The net increase of energy of the reservoir is (α – l)e. Here α is some numerical factor, positive or negative. Show that the effective Boltzmann factor for this abnormal system is given by

P(ε) ∞ exp[ –(1 – α)ℓ/τ]

This reasoning gives the statistical basis of the Overhauser effect whereby the nuclear polarization in a magnetic field can be enhanced above the thermal equilibrium polarization. Such a condition requires the active supply of energy to the system front an external source. The system is not its equilibrium, but is said to be in a steady stare.