Canonical ensemble Fixed parameters: T-temperature, V-volume, N-number of particles Thermostat at t System enclosed by impermeable diabatic walls Fluctuating parameter: E
Canonical ensemble: Fixed parameters: T - temperature, V - volume, N - number of particles System enclosed by impermeable diabatic walls Fluctuating parameter: E Thermostat at T . . . . .
Canonical ensemble Distribution function f(p, q)=exp( -h(pn, q)/kt)/z ZT,V,N): partition function(normalization factor) N N ZTVM-iJdp dg exp(Hp, q)kD 3N A=(2rB 2/m)/2-thermal wave length o-NSdr exp(F> 2ur r))-configuration integral Connection with thermodynamics: F(T,V,N=-kTIn(T,V,N) F(E, V,N): Helmholtz free energy F=E-TS
Canonical ensemble: Distribution function: f(p N , q N) = exp( - H(p N , q N)/kT)/Z Z(T, V, N): partition function (normalization factor). ( , , ) exp( ( , )/ ) ! 1 3 d d H k T h Z TV N p q p q N N N N N N = − Connection with thermodynamics: F(T, V, N) = - kT ln Z(T, V, N) F(E, V, N): Helmholtz free energy F = E - TS exp( ( , )) ! 1 = − j i i j i N r r r d u N Q = N Q 3 = (2p 2 /m)1/2 - thermal wave length - configuration integral