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同理: Sn-Nntn h(nC)Nnin Sn+sn=NAknh(AC.9c4m)片Nn如h6 (VnC.gn)+(+Wayknd22) SA+B-(NA+NB(NA+NB)Crm]+(NA+NB)kT ainq SA-5-S(Na)m) -Nxtnb(WACi9aNe72) -Wabwb(WwC.4.)m-Nne7f2), =(NA +NB)kB In(NA +NB)-NAkB In NA NBkB In NB 如果是不可区分的,则 5a=Nca小Na4) =Naah6Ga,9a+Naef22) Sa-Npkn hn(eC.q.m)+Nk SA +SB NAkB In(eCtqrqin )+NBkB In(eCtqrqin)+(NA NB)kBT =(NA+NB)h(eCqrm)+(NA+NB)kpg SA+B=(NA +NB)kB In(eCtqrqin)+(NA +NB)kBT同理: ( ) V T q S N k N C q q N k T         = + ln B B B ln B t r in B B ( ) ( ) V T q S S N k N C q q N k N C q q N N k T         + = + + + ln A B A B ln A t r in B B ln B t r in ( A B) B V T q S N N k N N C q q N N k T         + = + + + + ln A B ( A B) B ln[( A B) t r in ] ( A B) B ( ) ( ) A B B A B A B A B B B B B B t r in B B A B A t r in A B A B A B A B B A B t r in A B B ( ) ln( ) ln ln ln ln ln ln ln ( ) ln[( ) ] ( ) N N k N N N k N N k N T q N k N C q q N k T T q N k N C q q N k T T q S S S N N k N N C q q N N k T V V V = + + − −         − −         − −         + − − = + + + + 如果是不可区分的,则 ( ) V V T q N k eC q q N k T T q N C q q N k T N e S N k         = +         +        = ln ln ln ln A B t r in A B A t r in A B A A A B ( ) V T q S N k eC q q N k T         = + ln B B B ln t r in A B ( ) ( ) ( ) V V T q N N eC q q N N k T T q S S N k eC q q N k eC q q N N k T         = + + +         + = + + + ln ( )ln ( ) ln ln ln ( ) A B t r in A B B A B A B t r in B B t r in A B B V T q S N N k eC q q N N k T         + = + + + ln A B ( A B) B ln( t r in ) ( A B) B
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