Consider an extra degree of freedom called the demon which exchanges energy with a system consisting of many particles (spins). The demon exchanges energy with the system by choosing a particle (spin) at random and making a random change in its relevant coordinate. If the energy change of the system is negative, the "extra" energy is given to the demon and the trial change is accepted. If the energy change of the system is positive, the trial change is accepted if the demon has sufficient energy to give to the system. The only constraint is that Ed, the energy of the demon, must be greater than or equal to zero; otherwise, the trial change is not accepted.
The total energy of the demon plus the system is fixed. The demon can trade energy with the system as long as the demon's energy remains greater than zero.
Updated 20 March 2020.