PPT Slide
let us consider the case of thermal contact of two spin systems in magnetic field. The numbers of spins in system 1 is N1 and in system 2 is N2, the values of the spin excess 2s1, 2s2 may be different and can change but the total energy: U=U1(s1)+U2(s2)=-2mB(s1+s2)=-2mBs is fixed.
(g(N,s) is the multiplicity function of system S, g1,2 for system 1,2 respectively. If N1<N2 then in the sum -1/2N1? s1?1/2N1)
Example: Two spin systems in thermal contact
the most probable configuration of the system is where:
Nearly all accessible states of the combined system satisfy or nearly satisfy (*)!
Numerical example: N1=N2=1022; ?=1012; ?/N1=10-10 --> 2 ?2/N1=200 --> g1g2 reduced to e-400??10-174 of its maximal value!
We may expect to observe substantial fractional deviations from the most probable configuration only for a small system in thermal contact with a large system!