A Solution of the Equations of Statistical Mechanics
A Solution of the Equations of Statistical Mechanics
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We again use superscripts 'o' to denote this case . Thus (61) L°[w]=l+£ ^ lfl{^^, ... , q^)wioo, V->a3 in (lo) we obtain 16 (67) llm ^ M's "^l- V->ao V Now from (^7) (68) lim ^ V->oo V V and from (65) (69) lim — V->oo V^ exp V dq^ . . . Dq^ [-|uj dq^... Dq^. I It is clear from (69) that C = 1 for potentials (j)(r) which vanish sufficiently rapidly as i^>oo . We shall therefore Impose as a condition on (j) that the left side of (69) he equal to 1 for s = 1, 2, 5;, • • • • It follows now from (65...) that (70) f°(q^, ... , q^) = exp[-|u^] ; k = l, 2, ... .
The solution of (55) i'or non-zero density can be obtained from the zero density solution in a manner very similar to the procedure used in the non- equilibrium case. We begin with a trial form of the solution slightly more general than the one used in Section 3: (71) L[u] = L°[w]; w = a(u + -) ; a = const. By functional differentiation we have (72) 5u(q^)... 5u(q^) ^ 6w(q^) . . . 6w(q^) and substituting in (55) we see that the latter equation is satisfied because - 17 - In order to determine the constant, a, we observe first that since U is a function only of the coordinate differeftces (q.
What to read after A Solution of the Equations of Statistical Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by Robert M Lewis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
We again use superscripts 'o' to denote this case . Thus (61) L°[w]=l+£ ^ lfl{^^, ... , q^)wioo, V->a3 in (lo) we obtain 16 (67) llm ^ M's "^l- V->ao V Now from (^7) (68) lim ^ V->oo V V and from (65) (69) lim — V->oo V^ exp V dq^ . . . Dq^ [-|uj dq^... Dq^. I It is clear from (69) that C = 1 for potentials (j)(r) which vanish sufficiently rapidly as i^>oo . We shall therefore Impose as a condition on (j) that the left side of (69) he equal to 1 for s = 1, 2, 5;, • • • • It follows now from (65...) that (70) f°(q^, ... , q^) = exp[-|u^] ; k = l, 2, ... .
The solution of (55) i'or non-zero density can be obtained from the zero density solution in a manner very similar to the procedure used in the non- equilibrium case. We begin with a trial form of the solution slightly more general than the one used in Section 3: (71) L[u] = L°[w]; w = a(u + -) ; a = const. By functional differentiation we have (72) 5u(q^)... 5u(q^) ^ 6w(q^) . . . 6w(q^) and substituting in (55) we see that the latter equation is satisfied because - 17 - In order to determine the constant, a, we observe first that since U is a function only of the coordinate differeftces (q.
What to read after A Solution of the Equations of Statistical Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by Robert M Lewis to read onlineMoreLess
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