T - IfB
T - IfB
T - IfB
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Detailed balancedp( X , t)dt pY ( ) W( Y X) p( X) W( XY)YIn stationary state one should haveequilibrium distribution (Boltzmann)dpst( X , t)0dtY, p ( X) p ( X) p ( Y) W( Y X) p ( X) W( X Y)Yeqstsufficient condition is detailed balance:p ( Y) W( Y X) p ( X) W( X Y)eqYeqeqeq21Metropolis (M(RT) 2 ) peq( Y)AX ( Y) min1,peq( X) Boltzmann:1peq( X) eZTE( X )kTE( Y) E( X)EkTkTAX ( Y) min( 1, e ) min( 1, e )decreasesIf energy always acceptEincreases accept with probability .e - kT22