Конспект лекций по статистической физике. Коренблит С.Э - 8 стр.

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(1.2) ­¥®¡å®¤¨¬® â®ç­® §­ âì, ¯® ªà ©­¥© ¬¥à¥, ¤¢ á« £ ¥¬ëå ¨§ âà¥å.
 ¯à¨¬¥à, â¥à¬¨ç¥áª®¥ ¨/¨«¨ ª «®à¨ç¥áª¨¥ ãà ¢­¥­¨ï á®áâ®ï­¨ï ¢¨¤ :
      P = P (T; V ); ¨«¨ U = U (T; V ); S = S (T;!V );   !
                                                                  (1.3)
      ⮣¤ , ­ ¯à¨¬¥à: QT  = dS (T; ')  dT @S + d' @S ; (1.4)
                                             @T '      @' !T
                                                        @S ; (1.5)
      â® ¥áâì: (Q)' = T (dS )' = C'dT; ®âªã¤ : C' = T @T
                                                            '
{ ¥áâì ⥯«®¥¬ª®áâì ¤ ­­®£® ¯à®æ¥áá ' = const.
    Œ¥â®¤ë áâ â¨áâ¨ç¥áª®© 䨧¨ª¨ ¯à¨§¢ ­ë à¥è âì ¤¢ã¥¤¨­ãî § ¤ çã:
     ¢ëç¨á«ïâì â¥à¬®¤¨­ ¬¨ç¥áª¨¥ ãà ¢­¥­¨ï á®áâ®ï­¨ï (1.3), ¨á室ï
      ¨§ ¯à¥¤áâ ¢«¥­¨© ® ¬ˆªà®áª®¯¨ç¥áª®¬ ãáâனá⢥ á¨á⥬ë, { ¨§
      祣® ®­ á®á⮨⠨ ª ª ¢§ ¨¬®¤¥©áâ¢ãîâ ¬¥¦¤ã ᮡ®© ¥¥ ¬ˆªà®á®-
      áâ ¢«ïî騥;
     ¨áá«¥¤®¢ âì ¢§ ¨¬®¤¥©á⢨¥ ¬ˆªà®á®áâ ¢«ïîé¨å, ¨áå®¤ï ¨§ १ã«ì-
      â ⮢ ¨§¬¥à¥­¨ï ¬€ªà®áª®¯¨ç¥áª¨å ¢¥«¨ç¨­, ¢å®¤ïé¨å ¢ (1.3), (1.5).

2   ®­ï⨥ áâ â¨áâ¨ç¥áª®£® ­á ¬¡«ï
     Š« áá¨ç¥áª ï ¬¥å ­¨ç¥áª ï á¨á⥬ , ¨¬¥îé ï s á⥯¥­¥© ᢮¡®¤ë
®¡®¡é¥­­ëå ª®®à¤¨­ â ¨ ¨¬¯ã«ìᮢ (qit; pti)si=1 = X t (¥¥ ä §®¢ ï â®çª ),
¢ ®âáãâá⢨¥ ¤¨áᨯ ⨢­ëå ᨫ, ¢ ª®­¥ç­®¬ áç¥â¥, ¨ ­¥áâ 樮­ à­ëå
¢­¥è­¨å ¯®«¥©, ®¯¨áë¢ ¥âáï á¨á⥬®© ¨§ 2s £ ¬¨«ìâ®­®¢ëå ãà ¢­¥­¨©:
q_i = @H@p(X ) ; p_i = @H@q(X ) ; i = 1  s; ¨«¨ ªà ⪮: X_ t = V (X t); (1.6)
           i                 i
á ä㭪樥© ƒ ¬¨«ìâ®­ H (fqigs1; fpi gs1; t)  H (X ; t) =) H (X );       (1.7)
à¥è¥­¨ï ª®â®à®©: qi ) qit = q i(X 0; t); pi ) pti = pi(X 0; t); â® ¥áâì: (1.8)
X t = Gct(X 0); § ¢¨áï⠮⠭ ç «ì­ëå ¤ ­­ëå: X 0 = (qi0; p0i )si=1 ¯à¨ t = 0:
ˆá¯®«ì§ãï ï¢­ë¥ ¢ëà ¦¥­¨ï (1.6) ¤«ï 2s ª®¬¯®­¥­â ¢¥ªâ®à­®£® ¯®«ï ᪮-
à®á⥩ ä §®¢®© â®çª¨ V (X t), «¥£ª® ­ ©â¨ ãà ¢­¥­¨¥ ƒ ¬¨«ìâ®­ ¤«ï
«î¡®© ­¥§ ¢¨áï饩 ® ®â t ¤¨­ ¬¨ç¥áª®© ¢¥«¨ç¨­ë b(X ) ) b(X t):
         db (X  t) X  2s @b(X t) X   s @H @b         @H  @b  !
     b_  dt = x_ ti @x                  @p  @q     @q  @p    =)        (1.9)
                    i=1        i
                                n  i=1     i    i o   i   i
     =) V (X ) 
 rX b(X )  H (X ); b(X ) ; - ᪮¡ª ã áá®­ : (1.10)
                 t       t t            t       t