dE = Q W(1)EQWdE=0(E)E diE deEdiE diE 0(2)

diE=0 deE=dE=QW (3)

dS=diSdeS(4) diS: deS:diS diS 0(5)deS

diS=(diS)j (6)

(diS)j 0 (diS)1 0 (diS)2 0 [di(S1+S2)] 0(diS)

diS(1), diS(2)

diS(1) 0 diS(2) 0 [diS(1)diS(2)] 0

: (T,V,N)(T,p,V) : :

Tp (T,p)tdtt

t t+dt t+dt ttt+dt

, , .

t r :(n,E)

QV. Q tr = (t, r)(1)Q Q(t)=V (t,r) dV(2)QQjQ(t,r)

: Gaussdiv

(3)(4)dQ/dt(5)(5)

l n1,n2,nl i

1. :

mkA,A B,B C,C D,Dk(mol/t,V)i

():

TdS=dEpdVidni :s:e:v:dv=0.

de/dtdni/dtds/dt

(16)

Fi i:

t

(21)(18)442

1. JkXk

, ., ()Taylor, ,:

XJLX28

q=T

JkXiJk=Jk Xll=0,1,2,

TaylorX Lk,kXkJkLk,l

B0C0k1B0=k2C0 C0=B0(k1/k2) ArG

v=k1Bk2C

GA, A

J1J2J1L11X1L12X2 J2L21X1L22X2 L12L21

= J1X1+J2X2 = (L11X1L12X2)X1+(L21X1L22X2)X2 =L11X12+(L12+L21)X1X2+L22X22 0 L11>0; L22>0; (L12+L21)2 < 4L11L22 =kJkXx= k,kLk,kXkXk 0(3)

f=ax2+bxy+cy2 f=XAXfA

L11>0;

(L12+L21)2 < 4L11L22 (L12+L21)2 > 0 L11L22> 0 L11 > 0L22 > 0 L11 > 0L22 > 0 (L12+L21)2 < 4L11L22

2. ( Curie):

PrigogineCurie

A/T

CuriePrigogine

3.Onsager Lkk=Lkk (4) kJkkXkkJkkXkS

v1=k1A-k-1BA1=A-B v2=k2B-k-2CA2=B-C v3=k3C-k-3AA3=C-A =vk(Ak/T)=1/TvkAk =1/T[v1A1+v2A2+v3A3] =1/T[v1A1+v2A2+v3 (-A1-A2)]A3=(A1+A2) =1/T[(v1-v3)A1+(v2-v3) A2]

A1/T, A2/TX1X2J1=v1-v3X1=A1/T J2=v2-v3X2=A2/T

A,0= B,0= C,0 A1,0= A2,0= A3,0=0v1,0= v2,0= v3,0 k1A0=k-1B0 k2B0=k-2C0 k3C0=k-3A0

v1= k1A-k-1B=k1(A0+x)-k-1(B0+y) = k1A0- k-1B0+ k1x- k-1y = k1xk-1y(k1A0=k-1B0)

v1= k1xk-1yv2= k2yk-2zv3= k3zk-3x A1= AB = AB +A,0+B,0A,0B,0 = A,0B,0+ AB = AB A,0= B,0 A,0:A B,0:BC,0:CA= AA,0 B= BB,0

i,0=i0+RTln(pi,0/p0)i =i0+RTln(pi/p0)=i0+RTln[(pi/p0)(pi,0/pi,0)] =i0+RTln[(pi/ pi,0)(pi,0/ p0)] =i0+RTln(pi,0/ p0)+RTln(pi/ pi,0) = i,0+RTln(pi/ pi,0)AA= A,0+RTln(A/A0) = A,0+RTln[(A0+x)/A0] = A,0+RTln[1+(x/A0)]A= AA,0= RTln[1+(x/A0)]

A1=AB =RTln(1+x/A0)RTln(1+y/B0)x/A0

=J1X1+J2X2

L11=1/R(k1A0+k3C0)L12=k3C0/R L21=k3C0/RL22=1/R(k2B0+k3C0)L12=L21 Lkk=Lkk

:,,.,,.,.,,.,,,.,.,...

: . T1,T2. ,., , ,..

Onsager1931;Prigogine1945 :,.,,: XX, : JJ., X, J, XJ., . ,XJ, J., : .

:, : =JX+JX J=L11X+L12X J=L21X+L22X ,L12=L21: = L11X2+2L21XX + L22X2 ,X, X. X, X: /X= 2L21X+ 2L22X = 2(L21X+ L22X) = 2J : J=0:(/X)J()= 0

.:, L22>0, . , . ,, . :

l,k, , , :k = 1,2,3,P,

: , .:1, 1.2, 1.3, 1.

, , , ., , . : .

., , , ., .: , , . , , .

.Onsager, .

, , , .

, .

()

(Benard)T1T2

B-Z (Belorsov)1958ZhabotinskyBZ