{"id":8430,"date":"2009-03-20T17:11:00","date_gmt":"2009-03-20T17:11:00","guid":{"rendered":"http:\/\/melotopia.net\/b\/?p=8430"},"modified":"2009-03-20T17:11:00","modified_gmt":"2009-03-20T17:11:00","slug":"%eb%a7%88%eb%b2%95%ec%9d%98-%eb%b6%84%eb%b0%b0%ed%95%a8%ec%88%98-2","status":"publish","type":"post","link":"http:\/\/melotopia.net\/b\/?p=8430","title":{"rendered":"\ub9c8\ubc95\uc758 \ubd84\ubc30\ud568\uc218 2"},"content":{"rendered":"
\n \uc9c0\ub09c\ubc88 1\ubd80\uc5d0\uc11c
\n
\n $W=\\frac{n!}{k_1!k_2!…k_n!}$
\n
\n \ub77c\uace0 \ud588\ub2e4. W\ub294 \ub300\uccb4 \ubb34\uc2a8 \ub73b\uc778\uac00? W\ub294, n\uac1c\uc758 \uc785\uc790\ub97c N\uac1c\uc758 \uc0c1\ud0dc\uc5d0 $(k_1, k_2, k_3, …, k_N)$\uac1c\uc529 \ub123\uc5b4\uc11c \ucc44\uc6cc \ub123\ub294 \ubc29\ubc95\uc758 \uac00\uc9c0\uc218\uc774\ub2e4. \ubaa8\ub974\uaca0\uc73c\uba74 \uc9c1\uc811 \uc138\uc5b4 \ubcf4\uae30\ub97c…
\n
\n \uadf8\ub9ac\uace0 \uc5d0\ub108\uc9c0\ub791 \uc785\uc790\uc758 \uc218\uac00 \ubcf4\uc874\ub41c\ub2e4\uace0\ub3c4 \ud588\ub2e4.<\/p>\n

\uc774\uc81c, \uc544\uc8fc \ub9ce\uc740 $(k_1, k_2, k_3, …, k_N)$\uc758 \uac00\ub2a5\ud55c \uacbd\uc6b0 \uc911\uc5d0\uc11c, \uc5b4\ub5a4 \uac83\uc774 W\uac00 \uac00\uc7a5 \ud070 \uacbd\uc6b0\uc77c\uc9c0 \uc54c\uc544\ub0b4\uc57c \ud55c\ub2e4. \uc774\uac78 \uc54c\uc544\ub0b4\ub294 \uac83\uc740 \uc911\uc694\ud558\ub2e4. \uc65c\ub0d0\ud558\uba74, \uadf8\uac83\uc774 \ubc14\ub85c \uac00\uc7a5 \uadf8\ub7f4\ub4ef\ud558\uac8c \uc788\uc744 \ubc95\ud55c \uacbd\uc6b0\uc774\uae30 \ub54c\ubb38\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \ubcf4\uc790. \ud638\ud154\uc5d0 \ubc29\uc774 \uc544\uc8fc \ub9ce\uc774 \uc788\ub2e4. 1\uce35\ubd80\ud130 10\uce35\uae4c\uc9c0 \uc788\ub2e4\uace0 \ud558\uc790. \uc5ec\uae30\uc5d0 100\uba85\uc758 \uc190\ub2d8\uc774 \uc654\ub2e4. \uac01 \uce35\ub9c8\ub2e4 \uba87\uba85\uc529 \ub4e4\uc5b4\uac00 \uc788\ub294 \uac83\uc774 \uc790\uc8fc \ubc1c\uc0dd\ud560\uae4c? \uac00\uc7a5 \uc790\uc8fc \ubc1c\uc0dd\ud558\ub294 \uacbd\uc6b0\uac00 \uac00\uc7a5 \uc790\uc8fc \ubc1c\uacac\ub418\uc9c0 \uc54a\uc744\uae4c?
\n
\n \uac00\ub839, \uac01 \uce35\ub9c8\ub2e4 \uba87\uba85\uc529 \ub4e4\uc5b4\uac00 \uc788\ub294, \uadf8\ub7f0 \uac00\ub2a5\ud55c \uacbd\uc6b0\uc758 \uc218\uac00 \ubaa8\ub450 100\ub9cc\uac1c\ub77c\uace0 \ud558\uc790. \uadf8\ub7f0\ub370 1\uc5b5\ubc88\uc744 \uad00\ucc30\ud588\ub294\ub370, 1\uc5b5\ubc88\uc911\uc5d0\uc11c 9\ucc9c\ub9cc\ubc88\uc774 \uc5b4\ub5a4 1\uac1c \uc0c1\ud0dc\ub9cc \uad00\ucc30\ub418\uc5c8\ub2e4\uba74, \ubc14\ub85c \uadf8 \uc0c1\ud0dc\uac00 \uac00\uc7a5 \uc790\uc8fc \ubc1c\uc0dd\ud558\ub294 \uc0c1\ud0dc\ub77c\uace0 \ud560 \uc218 \uc788\uc9c0 \uc54a\uc744\uae4c?
\n
\n \uc774\ubd80\ubd84\uc744 \uc815\ud655\ud788 \uc774\ud574\ud574\uc57c \ud55c\ub2e4. \ud1b5\uacc4 \uc5ed\ud559\uc758 \uac00\uc7a5 \uae30\ubcf8\uc774\uae30 \ub54c\ubb38\uc774\ub2e4.
\n
\n \uc8fc\uc0ac\uc704\uac00 1\uac1c \uba74\uc740 1\uc774 \uc368\uc788\uace0, 5\uac1c \uba74\uc740 2\uac00 \uc368 \uc788\ub2e4\uace0 \ud558\uc790. \uc774 \uc8fc\uc0ac\uc704\ub294 \ub9ce\uc774 \ub358\uc838\ub3c4 \ub300\ubd80\ubd84 2\uac00 \ub098\uc62c \uac83\uc774\ub2e4. \ubb3c\ub860 1\/6\uc758 \ud655\ub960\ub85c 1\uc774 \ub098\uc624\uaca0\uc9c0\ub9cc. \uc544\ubb34\ud2bc, \uc804\uccb4 \uac00\ub2a5\ud55c 6\uac00\uc9c0 \uacbd\uc6b0 \uc911\uc5d0\uc11c 2\ub294 5\uac00\uc9c0 \uacbd\uc6b0\ub97c \ucc28\uc9c0\ud558\uace0 \uc788\ub2e4. \ubc14\ub85c \uc774\uac83\uc774\ub2e4. \ubaa8\ub4e0 \uac00\ub2a5\ud55c W\uc758 \uacbd\uc6b0 \uc911\uc5d0\uc11c, \uac00\uc7a5 \uacbd\uc6b0\uc758 \uc218\uac00 \ub9ce\uc740 \uc0c1\ud0dc \ubc30\uce58\uac00 \uac00\uc7a5 \uc790\uc8fc \ubc1c\uacac\ub418\ub294 \uacbd\uc6b0\uc774\uace0, \uc2e4\uc81c\ub85c \ubb3c\ub9ac \ud604\uc0c1\uc5d0\uc11c\ub294 \uc624\uc9c1 \uadf8 \uacbd\uc6b0\ubc16\uc5d0 \uad00\ucc30\ub418\uc9c0 \uc54a\ub294\ub2e4. \uc22b\uc790\uac00 \uc6cc\ub099 \ud06c\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\n

\ud558\uc9c0\ub9cc W\ub294 \ub108\ubb34 \ud06c\ub2e4. W\ub294 \uc9c4\uc9dc\ub85c \uc5c4\uccad\ub098\uac8c \ud070\ub370, n\uc5d0\ub2e4\uac00 100000\uc815\ub3c4\uc758 \uc218\ub97c \ub123\uc73c\uba74, W\ub294 \ub300\ub7b5 40\ub9cc \uc790\ub9ac\uc218\uc758 \uc218\uac00 \ub41c\ub2e4. \ud558\ubb3c\uba70, \uc2e4\uc81c \uc138\uacc4\uc758 \uc785\uc790 \uc218\ub294 10000000000000000000000\uac1c\ubcf4\ub2e4 \ud6e8\uc52c \ub9ce\ub2e4. \uc774 \uacbd\uc6b0 W\ub294 5000000000000000000000\uc790\ub9ac\uc758 \uc218\uac00 \ub41c\ub2e4. 5000000000000000000000\ub3c4 \uc544\ub2c8\ub77c, 5000000000000000000000\uac1c\uc758 \uc22b\uc790\ub97c \uc4f0\ub294 \uc218\ub2e4. \ucef4\ud4e8\ud130\uc5d0 \uc800\uc7a5\ud574\ubcfc \uc218\ub3c4 \uc5c6\ub2e4. \uc2e4\uc81c \uc138\uacc4\ub97c \ud45c\ud604\ud558\ub824\uba74 \uadf8\ubcf4\ub2e4 \ub354 \ud070 \uc22b\uc790\uac00 \ud544\uc694\ud558\ub2e4. \ub530\ub77c\uc11c W\ub97c \uc9c1\uc811 \uacc4\uc0b0\ud558\ub294\uac74 \uc5b4\ub5bb\uac8c \uc2dc\ub3c4\ud574\ubcfc \uc218\ub3c4 \uc5c6\ub2e4. \uadf8\ub798\uc11c \uc0ac\ub78c\ub4e4\uc740 \ub85c\uadf8 \ud568\uc218\ub97c \uc0ac\uc6a9\ud55c\ub2e4. W\uac00 \ucd5c\ub300\uac12\uc778 \uacbd\uc6b0\ub294 W\uc758 \ub85c\uadf8\uac12\ub3c4 \ucd5c\ub300\uac00 \ub41c\ub2e4. (\uc758\uc2ec\uac00\uba74 \uc9c1\uc811 \uc99d\uba85\ud574\ubcfc \uc218\ub3c4 \uc788\ub2e4.)<\/p>\n

W\uc758 \ub85c\uadf8\uac12\uc744 \ucd5c\ub300\ub85c \ub9cc\ub4dc\ub294, \uadf8\ub7f0 \uc0c1\ud0dc \ubc30\uce58\ub97c \ucc3e\uc544\ub0b4\ub294 \uac83\uc774 \uad00\uac74\uc774\ub77c\ub294 \uac83\uc774\ub2e4. \uadf8\ub7f0\ub370 \ubb38\uc81c\ub294 \uc81c\ud55c\uc870\uac74\uc774\ub2e4. \uadf8\ub798\uc11c \uacbd\uc6b0\uc758 \uc218\ub97c \ubc14\uafb8\uc9c0 \uc54a\uc73c\uba74\uc11c \uc81c\ud55c\uc870\uac74\uc744 \ub123\ub294 \ubc29\ubc95\uc744 \uc0dd\uac01\ud574 \ubcf4\uc790.
\n
\n $f(k_1, k_2, …, k_N)=ln(W)+\\alpha(n-\\sum k_i)+ \\beta(E-\\sum k_i E_i)$
\n
\n \uc5ec\uae30\uc11c $\\alpha$\ud558\uace0 $\\beta$\ub294 \uadf8\ub0e5 \uc22b\uc790\ub2e4. n\uc740 \uc54c\ub2e4\uc2dc\ud53c \uc804\uccb4 \uc785\uc790\uc758 \uc218\uc774\uace0 $k_i$\ub294 i\ubc88\uc9f8 \uc0c1\ud0dc\uc5d0 \ub4e4\uc5b4\uac00 \uc788\ub294 \uc785\uc790\uc758 \uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4. E\ub294 \uc804\uccb4 \uc5d0\ub108\uc9c0\uc758 \ud06c\uae30\uc774\uace0, $E_i$\ub294 i\ubc88\uc9f8 \uc0c1\ud0dc\uc5d0 \uc785\uc790\uac00 \ub4e4\uc5b4\uac14\uc744 \ub54c, \uadf8 \uc785\uc790\uac00 \uac16\uac8c \ub418\ub294 \uc5d0\ub108\uc9c0\uc758 \ud06c\uae30\uc774\ub2e4. \uc798 \uc0dd\uac01\ud574 \ubcf4\uba74, \uc804\uccb4 \uc785\uc790 \uc218\uc5d0\uc11c \uac01\uac01\uc758 \uc785\uc790 \uc218\ub97c \ubaa8\ub450 \ub354\ud55c \uac83\uc744 \ube90\uc73c\ub2c8 0\uc774 \ub418\uace0, \uc804\uccb4 \uc5d0\ub108\uc9c0\uc5d0\uc11c \uac01\uac01\uc758 \uc0c1\ud0dc\uc5d0 \ub4e4\uc5b4\uac04 \uc5d0\ub108\uc9c0\ub97c \ube90\uc73c\ub2c8 \uc5ed\uc2dc 0\uc774 \ub41c\ub2e4. \ub530\ub77c\uc11c \uc5b4\ub5a4 \ud568\uc218 \ud568\uc218 f\uc758 \ud06c\uae30\ub294 \ubcc0\ud558\uc9c0 \uc54a\uc558\ub2e4. \uc6b0\ub9ac\ub294 \uadf8\ub0e5 0\uc744 \ub354\ud588\uc744 \ubfd0\uc774\ub2e4.<\/p>\n

\uadf8\ub9ac\uace0 W\ub97c \uadfc\uc0ac\uc2dc\ucf1c\uc57c \ud55c\ub2e4. \uc2a4\ud138\ub9c1\uc758 \uba4b\uc9c4 \uacf5\uc2dd\uc744 \uc4f8 \ucc28\ub840\ub2e4.
\n
\n $ln(n!)=n*ln(n)-n$
\n
\n \ubb3c\ub860 \uc815\ud655\ud55c \uc2dd\uc740 \uc774\uac8c \uc544\ub2c8\uc9c0\ub9cc, \uc5b4\ucc28\ud53c \ub300\ucda9 \ud574\ub3c4 \uacb0\uacfc\ub294 \ub9de\ub294\ub2e4. (\uadf8\uac8c \ubc14\ub85c \ud1b5\uacc4\uc5ed\ud559\uc758 \uc2e0\ube44. \uc815\ud655\ud788 \uacc4\uc0b0\ud558\ub4e0 \ub300\ucda9 \uacc4\uc0b0\ud558\ub4e0 \ub2f5\uc740 \uac19\ub2e4.)
\n
\n f\uc5d0 \uc2a4\ud138\ub9c1 \uacf5\uc2dd\uc744 \uc801\uc6a9\ud558\uace0, \ub85c\uadf8 \uc548\uc5d0\uc788\ub294 \uc22b\uc790\uc758 \uacf1\uc740 \ub85c\uadf8 \ubc14\uae65\uc73c\ub85c \ube7c\uc11c \ub367\uc148\uc73c\ub85c \ubc14\uafd4\uc904 \uc218 \uc788\ub2e4\ub294 \uc131\uc9c8\uc744 \ud65c\uc6a9\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f8 \uc218 \uc788\ub2e4.
\n
\n $f(k_1, k_2, …, k_N)=n*ln(n)-n-\\sum (k_i*ln(k_i)-k_i)+\\alpha(n-\\sum k_i)+ \\beta(E-\\sum k_i E_i)$
\n
\n \ub300\ucda9 \ub367\uc148\ub07c\ub9ac \uc815\ub9ac\ud574 \uc8fc\uba74 \ub2e4\uc74c\uacfc \uac19\uc774 \ubcc0\ud55c\ub2e4.
\n
\n $f(k_1, k_2, …, k_N)=n*ln(n)-n+\\alpha n+\\beta n -\\sum (k_i *ln(k_i)-k_i-(\\alpha+\\beta E_i)k_i)$
\n
\n \uc880 \ubcf5\uc7a1\ud558\uc9c0\ub9cc \ub178\ud2b8\uc5d0 \ub2e4\uc2dc \uc815\ub9ac\ud574\uc11c \uc801\uc5b4\ub450\uae30 \ubc14\ub780\ub2e4.<\/p>\n

\uc5b4\uca0c\uac70\ub098, \uacf5\uc2dd\uc740 \ubcf5\uc7a1\ud558\uc9c0\ub9cc \uc6b0\ub9ac\ub294 \uc800\uac78 \ubbf8\ubd84\ud574\uc57c \ud55c\ub2e4. \uc65c\ub0d0\ud558\uba74, \ubbf8\ubd84\ud574\uc11c 0\ub418\ub294 \uc9c0\uc810\uc774 \ubc14\ub85c \uadf9\ub300\uac12 \ub610\ub294 \uadf9\uc18c\uac12\uc774 \ub418\uae30 \ub54c\ubb38\uc774\ub2e4. \uadf9\ub300\uc778\uc9c0 \uadf9\uc18c\uc778\uc9c0\ub294 \uc798 \ubab0\ub77c\ub3c4, \uc5b4\uca0c\ub4e0 \ubbf8\ubd84\ud558\uc790. \uc774\ub54c, \uac01\uac01\uc758 \uc0c1\ud0dc\uc5d0 \ub4e4\uc5b4\uac04 \uac1c\uc218\uc778 $k_i$\uc5d0 \ub300\ud574\uc11c \uc804\ubd80 \uadf9\ub300\uac12\uc774 \ub098\uc640\uc57c \ud558\ubbc0\ub85c, \ud3b8\ubbf8\ubd84\uc744 \uc368\uc57c \ud55c\ub2e4. \ud3b8\ubbf8\ubd84\uc740 \ud2b9\uc815\ud55c \ubcc0\uc218 1\uac1c\ub9cc \ube7c\uace0 \ub098\uba38\uc9c0\ub294 \uc0c1\uc218\ub85c \ucde8\uae09\ud558\ub294 \ubbf8\ubd84\ubc95\uc774\ub2e4.
\n
\n $\\frac{\\partial f}{\\partial k_i} = -ln(k_i)-(\\alpha+\\beta E_i)=0$
\n
\n \uac11\uc790\uae30 \ud56d\uc774 \ub9ce\uc774 \uc904\uc5b4\ub4e4\uc5c8\ub2e4. \uc65c\ub0d0\ud558\uba74 $k_i$\uc5d0 \ub300\ud55c \ubbf8\ubd84\uc774\ubbc0\ub85c n\uc5d0 \uad00\ud55c \ud56d\uc740 \uc804\ubd80 \uc0c1\uc218 \ucc98\ub9ac\ub418\uc5b4\uc11c \uc0ac\ub77c\uc84c\uae30 \ub54c\ubb38\uc774\ub2e4. \ub367\uc148\ub3c4 \ubaa8\ub450 \uc0ac\ub77c\uc84c\ub2e4. \uc65c\ub0d0\ud558\uba74 $k_i$\uc5d0 \ub300\ud55c \ubbf8\ubd84\uc774\ubbc0\ub85c \ud2b9\uc815\ud55c \ud56d\uc774 \uc544\ub2c8\uba74 \uc804\ubd80 \uc0c1\uc218 \ucc98\ub9ac\ub418\uc5b4\uc11c \uc0ac\ub77c\uc84c\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\n

\uc774\uc81c, \ubb38\uc81c\ub97c \ud480\uba74 \uae08\ubc29 \uc54c \uc218 \uc788\ub2e4.
\n
\n $k_i = exp(-(\\alpha+\\beta E_i))$
\n
\n \ubb54\uac00 \ubcf4\uc774\ub098?
\n
\n \uc7a0\uc2dc \ud3b8\ud558\uac8c \ubb36\uc5b4\uc8fc\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.
\n
\n $k_i = exp(-\\beta(E_i-\\mu))$
\n
\n \uc5ec\uae30\uc11c $\\mu$\ub294 \ud654\ud559\uc801 \uc704\uce58\uc5d0\ub108\uc9c0\ub77c\uace0 \ubd80\ub978\ub2e4. \uc7a0\uae50! \ud654\ud559\uc774 \uc65c \ud280\uc5b4\ub098\uc640?
\n
\n \uadf8\uac74 \ub098\ub3c4 \ubaa8\ub978\ub2e4. \uc544\ubb34\ud2bc, \uc911\uc694\ud55c\uac74 \uacfc\ud559\uc790\ub4e4\uc740 \uadf8 \uc22b\uc790\ub97c \uc774\ub984\ubd99\uc5ec\uc11c “\ud654\ud559\uc801 \uc704\uce58\uc5d0\ub108\uc9c0(Chemical potential)”\uc774\ub77c\uace0 \ubd80\ub978\ub2e4\ub294 \uac70\ub2e4. \ub098\uc911\uc5d0 \ub2e4\ub978 \uacfc\ud559\uc790\ub4e4\uacfc \uc624\ud574 \uc5c6\uc774 \uc758\uc0ac\uc18c\ud1b5\ud558\ub824\uba74 \uadf8 \ub2e8\uc5b4\uac00 \uadf8 \uac1c\ub150\uc778 \uac83\uc744 \uc54c\uc544 \ub450\uc790. \ucc38\uace0\ub85c, \uc800 \ud56d\uc740 \uc785\uc790\uc758 \uc218\uac00 \ubcf4\uc874\ub41c\ub2e4\ub294 \uc131\uc9c8\uc5d0\uc11c \ub098\uc654\ub2e4\ub294 \uac83\uc744 \uae30\uc5b5\ud574\uc57c \ud55c\ub2e4. \ub530\ub77c\uc11c \ud654\ud559\uc801 \uc704\uce58\uc5d0\ub108\uc9c0\uac00 \ubcc0\ud55c\ub2e4\uba74 \uc785\uc790\uc758 \uc218\uac00 \ubcc0\ud558\uac8c \ub41c\ub2e4\ub294 \uac83\uc744 \ub73b\ud55c\ub2e4.<\/p>\n

\uc800\uac83\uc740, \uc0ac\uc2e4\uc0c1\uc758 i\ubc88\uc9f8 \ubc29\uc5d0 $k_i$\uac1c\uc758 \uc785\uc790\uac00 \ub4e4\uc5b4\uac00 \uc788\uc744 \ud655\ub960\uc5d0 \ud574\ub2f9\ud55c\ub2e4. \uadf8\ub7ec\ub824\ub2c8 \ud558\uc790. $k_i$\ub97c \uc804\ubd80 \ub354\ud558\uba74 n\uc774 \ub418\uc5b4\uc57c \ud558\ubbc0\ub85c
\n
\n $k_i=n*exp(-\\beta E_i)\/Z$
\n
\n \ub77c\uace0 \uc4f8 \uc218 \uc788\ub2e4. \uc5ec\uae30\uc11c Chemical potential\uc740 \uc57d\ubd84\ub2f9\ud588\ub2e4\ub294 \uc0ac\uc2e4\uc744 \uc778\uc2dd\ud558\uae30 \ubc14\ub780\ub2e4. \uadf8\ub9ac\uace0 Z\ub294 1\ubd80\uc5d0\uc11c \uc124\uba85\ud588\ub358 \ubd84\ubc30\ud568\uc218\uc774\uace0, \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f4\ub2e4.
\n
\n $Z=\\sum exp(-\\beta E_i)$<\/p>\n

\ub9cc\uc57d \uc0c1\ud0dc\uac00 \uc5f0\uc18d\uc801\uc73c\ub85c \ubcc0\ud55c\ub2e4\uba74 \ub367\uc148\uc774 \uc544\ub2c8\ub77c \uc801\ubd84\uc73c\ub85c \ubc14\ub00c\uae34 \ud558\uc9c0\ub9cc, \uadf8\ub798\ub3c4 \uac1c\ub150\uc774 \ubc14\ub00c\ub294\uac74 \uc5c6\ub2e4.<\/p>\n

\uadf8\ub7f0\ub370 \uc774\uac8c \uc65c \ub9c8\ubc95\uc758 \ubd84\ubc30\ud568\uc218\ub0d0\uace0?<\/p>\n

\uadf8\uac74 3\ubd80\uc5d0\uc11c…
\n <\/p>\n

\n
\n
\n\"\uc2e0\uace0\"
\n<\/a>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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