Statistical Mechanics and Information Theory

Definition 1 (Spin Excess) For a system with N particles with spins ±m, the spin excess is given by how many particles more than N/2 have spin +m, i.e. S = N↑ − N2 where N↑ is the number of particles with spin +m. From Definition 1 and Equation (1) it follows that the total magnetic moment is given by M = 2mS. Theoretically, one could calculate the system’s magnetic moment at some point in time by using Newton’s laws for each particle (given the forces that act on each particle). However, as there are about 10 particles in a gram of matter, this is not very practical. A different approach would be to use statistical tools to find the probability of having a certain magnetic moment at some point in time. Since the total magnetic moment is a deterministic function of the spin excess, this is equivalent to finding the probability of a certain spin excess.