system , and their probabilities then we can predict any obouabk
< A > = -2 Pcn) Acn ) n estates
pcnldtp closed isolated system constant N ,
U , E , RCN,U ,El
, closed systems
d.s = ( Felde t (Fuku t (FuldN V , N E
,N YE
DE = Tds - Pd u t MdN
DE -_ Tds - Pdut Mdw T E is a function of 5,4N from S ECW, u, s ) state function
d. E -- ( ofnsldst (IT )dut¥u)dN u , N S
, N V, SThain rule
µ=&⇒s, N
measurable
, with
= E - TS " Helmholz free energy "
ACNE' E - TS
A- = E -TS dE=Td→ -Pdu
d. (A) =D ( E - TS) tµdN=dq-d¥ = DE - Idf - Sdt = - Sdt - Pdu t MDN
- S -- (off ), -P-CEIL, toffee -
A is like Energy
A- (N , YT ) fundamental "
(" thermodynamic potentials" )
Dekha :::: is: sum
§:%; H total = H system t H bath E total = Ess s t Ebafh constant
Stotal = Ssys t Sbath
E system = Hsys ( E) I arrangement of system
Db ( Nb , Vb , E Esys ) t f (Il -
prob of →
Sys to be ink
Swath = kg logRbl Nb, Ub, Eb) Eb = E total - E syst I Etot
Snath (Eb) ISbath (E total) = - Esyst
+ Coast e. ¥:: tHEe.slkb-a
Z const - Esys
kglog(RENNIEbath))
-
system discrete system Z = I e-
Enlkrst
QCN, u ,Tl = I
= fig e e- EAST I pwfdi SCHEMED I #
= tolde-""Iii. forcnn.esToystar
'
discrete Q= 2- rfenye.hn/krst
= Ng , e-E' Horst + Ne, e-
Ezlkst
E -
A- ( N, V,T) = E - TS
= e - t CEI ) (B) = Jd X BCN e-WHATLZ (E) = fdx Eqxyeitkxkkrst .L
Z = Jdx' e-HGHKist Z
BHAI n
g- = I
= - Cfp logZ -