MIT粒子统计学课程_Lec11.pdfVIP

III.HZerothOrderHydrodynamics

Asafirstapproximation,weshallassumethatinlocalequilibrium,thedensityf1at

eachpointinspacecanberepresentedasineq.(III.56),i.e.

n(�q,t)(�u(�2

0p−m�q,t))

p,�.(III.93)

f1(�q,t)=3/2exp−

2mkq,t)

(2πmkBT(�q,t))BT(�

Thechoiceofparametersclearlyenforcesd3p�f0=n,and�p/m��0=�u,asrequired.

1

AveragevaluesareeasilycalculatedfromthisGaussianweight;inparticular

0kBT

�cαcβ�=δαβ,(III.94)

m

leadingto

3

P0=nkBTδαβ,andε=kBT.(III.95)

αβ2

Sincethedensityf0isevenin�c,alloddexpectationvaluesvanish,andinparticular

1

0

�

h=0.(III.96)

Theconservationlawsinthisapproximationtakethesimpleforms



Dn=−n∂u



tαα

