뗚3뻭 뗚1웚 쇉 쓾 룟 횰 톧 놨 , No. 1 2001쓪 2퓂 LIAONING HIGHER VOCATIONAL TECHNICAL INSTITUTE JOURNAL Feb. 2001 컄헂뇠뫅ꎺ1009ꆪ7600ꎨ2001ꎩ01ꆪ0059ꆪ03 뛔탅쾢뗄첽쳖 낽 뫬 ꎨ뢧쮳횰튵벼쫵톧풺ꎬ쇉쓾 뢧쮳ꎺ113006ꎩ 햪 튪ꎺ닻쫶쇋퓚탅쾢싛훐뗄틢틥ꎬ늢럖뇰폃탅쾢풴뗄쯦믺뇤솿쫽뫍벸싊췆떼돶탅쾢폫컯샭뻟폐춳튻뇭듯쪽ꆣ 맘볼듊ꎺ탅쾢ꎻ컯샭 훐춼럖샠뫅ꎺG 201 컄쿗뇪쪶싫ꎺA 탅쾢ퟷ캪뿆톧뗄룅쓮ꎬ폐쯼ퟔ짭뗄쳘쫢탔ꎬ폐ퟅ좷쟐뗄몬틥ꎬ늢뿉뚨솿뛈솿ꆣퟮ돵ퟷ캪죈솦톧훐뗄튻룶쪮럖훘튪뗄첬몯쫽폐ퟅ좷쟐뗄컯샭틢틥ꆣ쿖죧뷱ꎬ쯼뗄펦폃틑풶풶뎬돶헢튻랶돫ꎬ맣랺퓋폃떽탅쾢싛ꆢ뿘훆싛뗈웤쯼쇬폲훐ꆣ평듋뛸돶쿖쇋탅쾢ꆣ뇊헟퇐뺿랢쿖ꎬ탅쾢늢쎻폐췑샫컯샭뛸떥뛀듦퓚ꎬ쯼뫍컯샭뿉폃튻춳튻뇭듯쪽살뇭쪾ꎬ쯼쏇뻟폐튻뚨솪쾵ꆣ 1ꎮ탅쾢뗄틢틥 탅쾢풴ꎨ볲돆탅풴ꎩ쫇닺짺쿻쾢ꎨ믲럻뫅ꎩ뫍쿻쾢탲쇐뗄풴ꆣ틔튻룶ퟮ볲떥뗄샫즢탅풴X캪 샽ꎬ웤룅싊뿕볤ꎨ볈탅풴뗄쫽톧쒣탍ꎩX:P[x1,x2,LxL,xi,q pp],웤훐pi쫇쫂볾:1L,pLxi붫튪랢짺뗄벸싊ꆣ죧,2,p,i,q맻쫂볾xi틑뺭랢짺ꎬ퓲룃쫂볾몬폐뗄탅쾢솿벴ퟔ탅쾢[1]캪Iꎨxiꎩ=ꦁkInpi ꎬ퓲탅풴뗄욽뻹탅쾢솿캪 qH(X)=ꦁK∑PInP (1) iii=1헢뻍쫇탅풴뗄탅쾢ꎬ쯼쫇뇭헷탅풴ퟜ쳥쳘헷뗄튻룶솿ꎬ뻟폐틔쿂틢틥ꆣ 탅쾢뇭쪾탅풴쫤돶쎿룶쿻쾢믲럻뫅쯹쳡릩뗄욽뻹탅쾢솿. 죧맻튻룶뗧싫평q훖럻뫅ퟩ돉ꎬ쎿훖럻뫅쿠뛔돶쿖뗄벸싊캪pi ꎬ튻룶뗧싫킯듸ퟅ튻뚨뗄탅쾢ꎬq퓲욽뻹쎿훖럻뫅킯듸뗄탅쾢솿캪 ꡃK∑PInP , 헢헽쫇룃탅풴뗄탅쾢ꆣ iii= 탅쾢뇭쪾탅풴쫤돶쿻쾢잰탅풴뗄욽뻹늻좷뚨탔 폐솽룶샫즢탅뫅풴XꆢYꎬ웤룅싊뿕볤럖뇰쫇X:[x1x2]Y:[y1y2P0,]():.ꎬ솽탅풴뗄탅쾢럖뇰x(Y):(x)=,Y(y)=, 평폚탅풴Y뗄솽훖쿻쾢돶쿖뗄벸싊뻹뗈ꎬ퓚탅풴쫤돶쿻쾢잰ꎬ닂닢y1뫍y2쓄튻룶믡돶쿖뗄늻좷뚨탔듳ꎬ쯼뗄탅쾢튲듳ꎻ뛸뛔X쫂쿈닂닢x1뫍x2쓄튻룶믡돶쿖ꎬ쯤좻폐늻좷뚨탔ꎬ떫닂훐x1뗄룅싊듳ꎬ쯹틔ꎬ탅풴X뗄늻좷뚨탔킡ꎬ웤탅쾢튲쿠뛔킡튻킩ꆣ탅쾢듳킡랴펳쇋탅풴쫤돶쿻쾢잰욽뻹늻좷뚨뗄돌뛈ꆣ탅쾢듳ꎬ탅풴뗄늻좷뚨탔뻍듳ꎻ랴횮ꎬ늻좷뚨탔뻍킡ꆣ 탅쾢뇭헷쫂볾랢짺뗄쯦믺탔 죧짏쏦솽룶탅풴XꆢYꎬ닂닢y1뫍y2뗄쯦믺탔듳ꎬ탅풴Y뗄탅쾢튲듳ꎻ뛸닂닢x1뫍x2뗄쫕룥죕웚ꎺ2000ꆪ12ꆪ18
60 쇉 쓾 룟 횰 톧 놨 뗚3뻭 쯦믺탔킡ꎬ탅쾢튲킡ꆣ 2ꎮ탅쾢폫컯샭뻟폐춳튻뇭듯쪽 컯샭뗄틢틥ꎺ 죈솦톧훐ꎬ쫇욽뫢첬죈솦톧뗄튻룶첬몯쫽ꎬ쯼뗄뚨틥캪2 S=dQ∫1T+S0웤훐ꎬ1ꆢ2쫇솽룶욽뫢첬ꎬ믽럖슷뺶퇘ퟅ죎틢뿉쓦맽돌ꎬT캪죈풴컂뛈ꎬdQ쫇쒳튻캢킡맽돌훐쾵춳컼쫕뗄죈솿ꆣ 퓶풭샭쫇죈솦톧뗚뛾뚨싉뗄쫽톧뇭듯쪽 퓶풭샭쫇쮵ꎬ튻룶맂솢쾵춳뗄죎뫎ퟔ랢맽돌ꎬ쾵춳뗄폀늻복킡ꎬ벴∆Sꇝ0.평듋뿉쮵쏷죈솦톧뗚뛾뚨싉뗄헽좷탔ꆣ춬쪱ꎬ튲룸돶쇋에뚨맂솢쾵춳늻뿉쓦맽돌뷸탐랽쿲뗄ힼ퓲ꎬ볈횻쓜쿲퓶볓랽쿲뷸탐 퓚죈솦톧훐뗄ꆰ떼퇝ꆱퟷ폃 맂솢쾵춳뗄죎뫎ퟔ랢맽돌뚼쫇평럇욽뫢첬쿲욽뫢첬ꎬ듯떽욽뫢첬뇣늻퓚뇤뮯쇋ꎬ틲듋ꎬ욽뫢첬쫇ퟮ듳ꆣ첬몯쫽벫듳횵폖뿉ퟷ캪에뚨ퟔ랢맽돌뷸탐쿞뛈뗄ힼ퓲ꎬ평듋튲뿉떼돶쾵춳뒦폚욽뫢첬쪱뗄룷훖에뻝ꆣ 쫇쾵춳욽뫢돌뛈뗄솿뛈 튻룶맂솢쾵춳ꎬ쾵춳욽뫢돌뛈풽뗍ꎬ뻍풽킡ꎻ욽뫢돌뛈풽룟ꎬ뻍풽듳ꎻ떱쾵춳췪좫듯욽뫢쪱ꎬ듯떽벫듳횵ꆣ 쫇컯훊쾵춳믬싒뛈뗄솿뛈 춳볆컯샭훐ꎬ늣뛻춳볆샭싛믲솿ퟓ춳볆샭싛뚼폐 S=kInꚸ (2) 볈늣뛻싼맘쾵쪽ꆣK쫇늣뛻싼뎣쫽ꎬꚸ 쫇쾵춳뗄캢맛ힴ첬쫽ꆣ퓚뫪맛쳵볾늻뇤뗄쟩뿶쿂ꎬ쾵춳뻟폐듳솿뗄캢맛ힴ첬ꆣ떱쾵춳뒦폚욽뫢쪱ꎬ캢맛첬쫽풽뛠ꎬ쾵춳풽ꆰ믬싒ꆱꎬ뻍풽듳ꎻ럱퓲ꎬ뻍풽킡ꆣ듓캢맛틢틥짏붲ꎬ쫇컯훊쾵춳컞탲탔뫍믬싒뛈뗄솿뛈ꆣ 탅쾢폫컯샭뻟폐춳튻뇭듯쪽 죧맻냑튻룶탅풴떱ퟶ컯훊쾵춳ꎬ뿉쓜쫤돶뗄쿻쾢풽뛠ꎬ탅풴뗄쯦믺탔뫍늻좷뚨탔풽듳ꎬ풽컉싒ꎬ튲풽듳ꆣ쯹틔ꎬ탅쾢폫컯샭튻퇹ꎬ뚼뿉뾴ퟷ컯훊쾵춳컉싒돌뛈뗄솿뛈ꎬ쯼쏇펦뻟폐춳튻뇭듯쪽ꎬ볈뿉뇭쪾돉ꎨ1ꎩ쪽뫍ꎨ2ꎩ쪽탎쪽ꆣ 폃탅풴뗄쯦믺뇤솿쫽뇭쪾탅쾢 짨R쫇탅풴뿉쓜쫤돶뗄쿻쾢쫽ꎨ볈쯦믺뇤솿쫽ꎩꎬ폐튻훖쏜싫쫇평N룶q훖럻뫅ퟩ돉ꎬ벴qN=∑Ni ꎬ퓲q훖럻뫅퓚N룶캻훃짏뗄ퟩ뫏랽쪽ꆢ볈탅풴뗄쯦믺뇤솿쫽캪 i=1N! R=∏ (3) N!ii쎿훖ퟩ뫏킯듸ퟅ튻뚨탅쾢ꎬ뻝탅쾢뗄뚨틥ꎬ퓚쎿훖ퟩ뫏훐ꎬ쎿훖럻뫅킯듸뗄욽뻹탅쾢솿캪ꎺqH=ꦁK∑PInP (4) iii=1웤훐ꎬNPii= 쫇뗚i훖럻뫅돶쿖뗄벸싊ꆣ N떱Ni뫜듳쪱ꎬ평Stirling릫쪽InNiꎡ=Ni(InNiꎭ1)뫍InNiꎡ=N(InNꎭ1),쪽ꎨ4ꎩ뿉뷸튻늽킴돉
뗚1웚 낽 뫬ꎺ뛔탅쾢뗄첽쳖 61 KN! H=()In(N∏ ) (5) N!ii붫쪽ꎨ3ꎩ듺죫(5)ꎬ늢쇮k’K=퓲 NH=k’InR (6) 평ꎨ6ꎩ쪽뾴돶ꎬ탅쾢폫컯샭뚼뿉뇭쪾돉늣뛻싼맘쾵쪽뗄탎쪽ꆣ 폃벸싊럖늼뇭쪾컯샭 뻝춳볆컯샭뗄쾵춳샭싛[2]ꎬ평튻훖좫춬솣ퟓퟩ돉뗄뾪럅쾵춳ꎬ폐솽룶뇤솿N뫍ESꎬ럖뇰뇭쪾쾵춳뗄솣ퟓ쫽뫍뒦폚S솿ퟓ첬뗄쓜솿ꎬ쾵춳뒦폚캢맛첬ꎨN,sꎩ뗄벸싊캪 PN,S=1Zexp(ꦁaN−bEs) (7) 웤훐ꎬZ=∑exp(ꦁaN−bEs) ,쾵춳뗄캪: N,S S=K(InZ∂InZ−∂InZ-aabb)=K[InZ-(aN−bE∂∂s)] =-K∑1Zexp(ꦁaN−bEs)In[1Zexp(ꦁaN−bEs) ] (8) N,S 붫ꎨ7ꎩ쪽듺죫ꎨ8ꎩ쪽ꎬ퓲쾵춳뗄뇭쪾캪S=-K∑PN,SInPN,S ,춬샭ꎬ죧맻볙짨쾵춳뒦폚N,Sf뗚i룶캢맛첬쪱ꎬ폐f룶뇤솿ꎨx1,x2,…xj,xfꎩ,쎿룶캢맛첬돶쿖뗄벸싊캪Pi=1xp(-∑bjxj) .iZeiiiij=1f웤훐ꎬZ=∑exp(−∑bjxj).춬퇹뿉횤쏷ꎬ룃컯훊쾵춳뿉뇭쪾돉S=-K∑PInPiii ,폫탅쾢튻ij=1i=1퇹ꎬ컯샭튲뿉폃벸싊럖늼살뇭쪾ꆣ 3ꎮ뷡싛 탅쾢폫컯샭뻟폐춳튻뇭듯쪽ꎬ뇭쏷쯼폫컯샭튻뚨뻟폐쒳훖솪쾵ꎬ퓚튻뚨돌뛈짏쫇춳튻뗄ꆣ늻뷶듙뷸쇋죈솦톧뫍춳볆컯샭ퟔ짭랢햹ꎬ쯼뗄펦폃틑풶풶뎬돶헢튻랶돫ꎬ횱뷓째죫떽탅쾢싛ꆢ뿘훆싛ꆢ룅싊싛ꆢ쳬쳥컯샭ꆢ폮훦싛짵훁짺쏼뗈쇬폲ꆣ뿉틔쿠탅ꎬ헢룶뢳폐짺쏼뗄룅쓮붫믡믱뗃룼캪맣랺뗄펦폃ꆣ 닎 뾼 컄 쿗 [1] 샮 삥ꎮ퓶풭샭 뢺풭샭 죋샠퇝뮯ꎮ냙뿆횪쪶ꎬ1990ꎬ10 [2] 췴횾돏ꎮ죈솦톧춳볆컯샭ꎮ놱뺩ꎺ룟뗈뷌폽돶냦짧ꎬ1985 The Study of Information Entropy AO Hong (Fushun Vocational Technology Institute, Fushun Liaoning: 113006) 䅢獴牡捴ꎺIn this paper, the meanings of entropy in information theory are discussed. A unified formula to calculate information entropy and physics entropy is deduced with using random variable numbers of information resource and possibility. 䭥礠坯牤?ꎺInformation Entropy; Physics Entropy ꎨ퓰죎뇠벭ꎬ뢧쮳횰풺ꎺ몫짙훒ꎩ
