... 97 10 0 10 0 10 2 10 3 10 5 10 5 10 7 11 0 11 0 11 0 11 2 11 2 11 4 11 5 11 7 Classical Limit of Statistical Mechanics 4 .1 Classical Hamiltonian 4 .1. 1 Hamilton-Jacobi ... finds σi = −p1 log p1 − (1 − p1 ) log (1 − p1 ) · ¸ p2 p2 p3 p3 log − log + (1 − p1 ) − − p1 − p1 − p1 − p1 = −p1 log p1 − p2 log p2 − p3 log p3 − (1 − p1 − p2 − p3 ) log (1 − p1 ) = σ (p1 , p2 , ... log q2 − − qM1 log qM1 + p1 log p1 , p1 σ (1. 26) µ ¶ qM1 +1 qM1 +2 qM1 +M2 p2 σ , , , p2 p2 p2 = −qM1 +1 log qM1 +1 − qM1 +2 log qM1 +2 − − qM1 +M2 log qM1 +M2 + p2 log p2 , (1. 27) etc., thus...