Let A, be a system of four spin ½ particles with moments µ (or s.) all aligned with a magnetic field B such that the energy E= - 4µB. Let Az be a second system of four spin ½ particles (isolated from A,) with moments all antialigned with respect to B such that the energy E= 4µB. (a) What is the multiplicity 2 and entropy S of each system for this states (A1 separated from A;)? (c) Suppose you then isolate the two systems at some later time. What is the probability that A, has energy – 4µB? (Hìnt: When you isolate A¡ you pick A¡ with only one possible configuration out of Q (N,n1) it forms with the combined system such that all the isolated spins are up)

Let A, be a system of four spin ½ particles with moments µ (or s.) all aligned with a magnetic field B such that the energy E= - 4µB. Let Az be a second system of four spin ½ particles (isolated from A,) with moments all antialigned with respect to B such that the energy E= 4µB. (a) What is the multiplicity 2 and entropy S of each system for this states (A1 separated from A;)? (c) Suppose you then isolate the two systems at some later time. What is the probability that A, has energy – 4µB? (Hìnt: When you isolate A¡ you pick A¡ with only one possible configuration out of Q (N,n1) it forms with the combined system such that all the isolated spins are up)