[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/5197#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/5197","headline":"\u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f-Wikipedia","name":"\u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f-Wikipedia","description":"before-content-x4 \u4e00 \u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f \u73fe\u8c61\u5b66\u7684\u306b\u6b63\u5f53\u5316\u3055\u308c\u305f\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u3042\u308a\u3001\u30b7\u30b9\u30c6\u30e0\u306e\u78ba\u7387\u306e\u6642\u9593\u767a\u9054\u3092\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002 after-content-x4 \u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f\u306f\u3001\u500b\u5225\u306e\u91cf\u306e\u72b6\u614b\u304b\u3089\u306e\u6761\u4ef6\u3067\u3059\u3002 dPkdt= \u2211\u2113\u2260k\uff08 Tk\u2113P\u2113 – T\u2113kPk\uff09\uff09 \u3002 {displaystyle {frac {mathrm {d} p_ {k}} {mathrm {d}","datePublished":"2023-12-13","dateModified":"2023-12-13","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/caa257589a5d833ec7d53beb2831b448c0b53c32","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/caa257589a5d833ec7d53beb2831b448c0b53c32","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/5197","wordCount":4950,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u4e00 \u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f \u73fe\u8c61\u5b66\u7684\u306b\u6b63\u5f53\u5316\u3055\u308c\u305f\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u3042\u308a\u3001\u30b7\u30b9\u30c6\u30e0\u306e\u78ba\u7387\u306e\u6642\u9593\u767a\u9054\u3092\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f\u306f\u3001\u500b\u5225\u306e\u91cf\u306e\u72b6\u614b\u304b\u3089\u306e\u6761\u4ef6\u3067\u3059\u3002 dPkdt= \u2211\u2113\u2260k\uff08 Tk\u2113P\u2113 –  T\u2113kPk\uff09\uff09 \u3002 {displaystyle {frac {mathrm {d} p_ {k}} {mathrm {d} t}} = sum _ {ell neq k}\uff08t_ {kell} p_ {ell} -t_ {ell k} p_ {k}\uff09\u3002}}} \u3057\u305f\u304c\u3063\u3066        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4p k{displaystyle p_ {k}} \u78ba\u7387\u306f\u3001\u30b7\u30b9\u30c6\u30e0\u304c\u5dde\u306b\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059 k {displaystyle k} \u914d\u7f6e\u3055\u308c\u3066\u3044\u307e\u3059 t k\u2113{displaystyle t_ {kell}} \u6761\u4ef6\u306e\u79fb\u884c\u7387 \u2113 {displaystyle ell} \u72b6\u614b\u306b        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4k {displaystyle k} \u306f\u3002\u540c\u69d8\u306b\u3001\u9023\u7d9a\u6761\u4ef6\uff08\u304a\u3088\u3073\u5bfe\u5fdc\u3059\u308b\u78ba\u7387\uff09\u306e\u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f\u306f\u3001\u500b\u5225\u306e\u6761\u4ef6\u3068\u540c\u69d8\u306b\u5408\u8a08\u3067\u306f\u306a\u304f\u7d71\u5408\u306e\u307f\u3067\u306e\u307f\u7b56\u5b9a\u3067\u304d\u307e\u3059\u3002 \u78ba\u7387\u7406\u8ad6\u3067\u306f\u3001\u3053\u308c\u306fChapman-Kolmogorow\u65b9\u7a0b\u5f0f\u306e\u7d71\u5408\u3055\u308c\u305f\u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f\u304c\u306b\u5bfe\u5fdc\u3059\u308b\u9023\u7d9aMarkow\u30d7\u30ed\u30bb\u30b9\u3068\u898b\u306a\u3055\u308c\u307e\u3059\u3002 [\u521d\u3081] \u3002 \u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3067\u3059 t \u2113k{displaystyle t_ {ell k}} \u5bfe\u79f0\u6027\uff08\u3064\u307e\u308a\u3001\u3059\u3079\u3066\u306e\u5fae\u8996\u7684\u9077\u79fb\u306f\u53ef\u9006\u7684\u3067\u3042\u308a\u3001\u4e21\u65b9\u5411\u306e\u79fb\u884c\u7387\u306f\u540c\u3058\u3067\u3059\uff09\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 Tk\u2113= T\u2113k\u3001 {displaystyle t_ {kell} = t_ {ell k}\u3001} \u3057\u305f\u304c\u3063\u3066\uff1a dPkdt= \u2211\u2113Tk\u2113\uff08 P\u2113 –  Pk\uff09\uff09 \u3002 {displaystyle {frac {mathrm {d} p_ {k}} {mathrm {d} t}} = sum _ {ell} t_ {kell}\uff08p_ {ell} -p_ {k}\uff09\u3002}} \u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f\uff08integro\u5dee\u52d5\u65b9\u7a0b\u5f0f\uff09\u306f\u3001\u7121\u9650\u79e9\u5e8f\u306e\u90e8\u5206\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u3057\u3066\u8868\u73fe\u3067\u304d\u307e\u3059\u3002 [2] \u3002 \u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f\u306f\u3001\u30b3\u30eb\u30e2\u30b4\u30ed\u30d5\u524d\u65b9\u7a0b\u5f0f\u306e\u540c\u7b49\u306e\u5909\u63db\u3067\u3059\u3002\u6642\u9593\u306e\u306a\u3044\u30de\u30fc\u30b3\u30fc\u30d7\u30ed\u30bb\u30b9\u306b pij\uff08 t \uff09\uff09 \uff1a= p \uff08 \u30d0\u30c4 \uff08 s + t \uff09\uff09 = j ‘ \u30d0\u30c4 \uff08 s \uff09\uff09 = \u79c1 \uff09\uff09 {displaystyle p_ {ij}\uff08t\uff09\uff1a= p\uff08x\uff08s+t\uff09= jmid x\uff08s\uff09= i\uff09}} \u6761\u4ef6\u304b\u3089\u306e\u9077\u79fb\u306e\u9077\u79fb\u78ba\u7387 \u79c1 {displaystyle i} \u72b6\u614b\u306b\u3042\u308a\u307e\u3059 j {displaystyle j} \u3002\u3042\u306a\u305f\u306f\u5c0f\u3055\u306a\u5024\u306b\u306a\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 d t {displaystyle delta t} \u5f62\u3067 p ij\uff08 d t \uff09\uff09 = d ij+ Q ijd t + o \uff08 d t \uff09\uff09 {displaytle p_ {ij}\uff08t\u306e\uff09= dellow _ {ij} el _ {ij} ofel t+o\uff08t\uff09}}\u3002 \u8868\u73fe\u3057\u307e\u3059 Q = \uff08 Q ij\uff09\uff09 {displaystyle q =\uff08q_ {ij}\uff09} \u5f37\u5ea6\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u3001\u305d\u306e\u30a8\u30f3\u30c8\u30ea\u304c\u30e1\u30a4\u30f3\u306e\u5bfe\u89d2\u7dda\u304b\u3089\u96e2\u308c\u305f\u30d7\u30ed\u30bb\u30b9\u306e\u30b8\u30e3\u30f3\u30d7\u30ec\u30fc\u30c8\u3067\u3059\u3002\u30a8\u30f3\u30c8\u30ea\u306b Q kk{displaystyle q_ {kk}} \u4e3b\u306a\u659c\u3081\u306f\u5426\u5b9a\u3055\u308c\u305f\u5024\u3092\u53d6\u308a\u307e\u3059  –  Q kk{displaystyle -q_ {kk}} \u30b8\u30e3\u30f3\u30d7\u30ec\u30fc\u30c8\u306e\u65b9\u6cd5\u306e\u5f79\u5272\u3001\u305d\u306e\u76f8\u4e92\u4fa1\u5024  –  \u521d\u3081 \/ Q kk{displaystyle -1\/q_ {kk}} \u6307\u6570\u95a2\u6570\u7684\u306b\u5206\u914d\u3055\u308c\u305f\u6ede\u5728\u671f\u9593\u306e\u671f\u5f85\u5024\u306f\u5dde\u306b\u3042\u308a\u307e\u3059\u3002\u3068 d ij{displaystyle delta _ {ij}} Kronecker Delta\u306f\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u304b o \uff08 d t \uff09\uff09 {displaystyle o\uff08delta t\uff09} Landau\u8868\u8a18\u3067\u3059\u3002\u9077\u79fb\u78ba\u7387\u3092\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306b\u6301\u3061\u8fbc\u307f\u307e\u3057\u3087\u3046 p \uff08 t \uff09\uff09 \uff1a= \uff08 p ij\uff08 t \uff09\uff09 \uff09\uff09 {displaystyle P\uff08t\uff09\uff1a=\uff08p_ {ij}\uff08t\uff09\uff09} \u4e00\u7dd2\u306b\u3001\u305d\u306e\u6642\u9593\u7684\u767a\u9054\u306f\u30b3\u30eb\u30e2\u30b4\u30ed\u30d5\u306e\u3088\u3046\u306a\u524d\u65b9\u65b9\u7a0b\u5f0f\u306b\u3088\u3063\u3066\u8a18\u8ff0\u3055\u308c\u3066\u3044\u307e\u3059 dP(t)dt= p \uff08 t \uff09\uff09 Q \u3001 {displaystyle {frac {mathrm {d} p\uff08t\uff09} {mathrm {d} t}} = p\uff08t\uff09q\u3001} \u3053\u3053\u3067\u3001\u521d\u671f\u5024 p \uff08 0 \uff09\uff09 {displaystyle P\uff080\uff09} \u30e6\u30cb\u30c3\u30c8\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u3067\u3059\u3002 [3] \u30de\u30c8\u30ea\u30c3\u30af\u30b9\u6307\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u306f\u30d5\u30a9\u30fc\u30e0\u306b\u3042\u308a\u307e\u3059 p \uff08 t \uff09\uff09 = exp \u2061 \uff08 t Q \uff09\uff09 {displaystyle p\uff08t\uff09= exp\uff08tq\uff09} \u4ee3\u8868\u3059\u308b\u3002\u3053\u306e\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u306f\u3001\u30c1\u30e3\u30c3\u30d7\u30de\u30f3\u30b3\u30eb\u30e2\u30b4\u30fc\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059 p \uff08 s + t \uff09\uff09 = p \uff08 s \uff09\uff09 p \uff08 t \uff09\uff09 {displaystyle p\uff08s+t\uff09= p\uff08s\uff09p\uff08t\uff09} \u3002 \u5f37\u5ea6\u884c\u5217\u306e\u5404\u30e9\u30a4\u30f3\u5408\u8a08\u304c\u30bc\u30ed\u3067\u3042\u308b\u305f\u3081\u3001\u9069\u7528\u3055\u308c\u308b\u305f\u3081 Q kk=  –  \u2211 l\u2260kQ kl{displaytle q _ {{kk} =  –  sum _ {{lneq k} q_ {kl}} \u3002\u3053\u308c\u3092\u4f7f\u7528\u3057\u3066\u5909\u63db\u3067\u304d\u307e\u3059 dpikdt= \u2211lpilqlk= \u2211l\u2260kpilqlk+ pikqkk= \u2211l\u2260k\uff08 pilqlk –  pikqkl\uff09\uff09 \u3002 {displayst {smathrm {{drm {d} {my {wik} {d}} {d} {d} {d}}\u3002_ {kl}\uff09\u3002 \u3042\u306a\u305f\u304c\u7f6e\u304d\u63db\u3048\u305f\u5834\u5408 p k\uff1a= p ik{displaystyle p_ {k}\uff1a= p_ {i}} \u305d\u3057\u3066\u3001\u5f37\u5ea6\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u305d\u306e\u8ee2\u7f6e\u3092\u4ecb\u3057\u3066\u3044\u307e\u3059 t kl\uff1a= Q lk{displaystyle t_ {kl}\uff1a= q_ {lk}} \u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f\u306e\u5f62\u5f0f\u306f\u3001\u7d50\u679c\u3092\u8aac\u660e\u3057\u307e\u3057\u305f\u3002 \u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u3001\u7d71\u8a08\u7684\u306b\u89b3\u5bdf\u53ef\u80fd\u306a\u6642\u9593\u306e\u767a\u9054\u3092\u8aac\u660e\u3067\u304d\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u4f7f\u7528\u3059\u308b\uff1a \u3068 \uff08 \u30d0\u30c4 \uff09\uff09 \uff08 t \uff09\uff09 = \u2211x\u30d0\u30c4 Px\uff08 t \uff09\uff09 \u27f9 dE(x)dt\uff08 t \uff09\uff09 = \u2211x\u30d0\u30c4 dPxdt\uff08 t \uff09\uff09 {displaystyle e\uff08x\uff09\uff08t\uff09= sum _ {x} xp_ {x}\uff08t\uff09\u306f{frac {mathrm {d} e\uff08x\uff09} {mathrm {d} t}}}\uff08t\uff09= sum _ {x} x {frac {mathrm {x} {x} {x} {x} {x} {x} {d} \uff09} \u3001 \u30de\u30b9\u30bf\u30fc\u65b9\u7a0b\u5f0f\u306f\u80cc\u9762\u3067\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3092\u4f7f\u7528\u3057\u3066\uff08\u30b8\u30e3\u30f3\u30d7\u30e2\u30fc\u30e1\u30f3\u30c8\u306e\u5c0e\u5165\u5f8c\uff09\u3001\u7dda\u5f62\u5fdc\u7b54\u7406\u8ad6\u3092\u5c0e\u51fa\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 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