Re: [MATH/Phys.] Equili. & Opt.

[Aiviet Nguyen <aiviet@cat.syr.edu>]

Hi Anh Vu,

  Xem chu+`ng ca'i ca'ch nghi~ chuye^n toa'n va^~n co`n ta'c du.ng la('m.
Ca'i su+. tie^n dde^` hay ddi.nh ly' nhie^`u khi no'i kho+i kho+i the^' 
na`y thi` kho' pha^n bie^.t.

   Thu+.c ra nghie^m chi?nh thi` no' la` chuye^.n ddi.nh nghi~a va` 
ddie^`u kie^.n ca^`n va` ddu?. Mo.i ddie^`u kie^.n ca^`n va` ddu? ( 
mo^.t loa.i ddi.nh ly') dde^`u co the^? la^'y la`m ddi.nh nghi~a va` 
ngu+o+.c la.i.

  Trong tru+o+`ng ho+.p na`y thi` no' ra the^' na`y: Mo.i he^. holonom
dde^`u dda.t ca^n ba(`ng khi va` chi? khi na(ng lu+o+.ng dda.t cu+.c tie^?u.

Ne^'u la^.t ddi.nh nghi~a cu?a he^. holonom thi` se~ tha^'y la` he^. ca^n 
ba(`ng khi na(ng lu+o+.ng dda.t cu+.c tie^?u...

Vi` va^.y thu+.c ra no' cha(?ng pha?i ddi.nh ly' gi` he^'t . Tho^ng tin 
no' chi? ra la` to^`n ta.i mo^.t so^' he^. ( ha^`u he^'t ca'c he^. trong 
thu+.c tie^~n) dda.t ca^n ba(ng khi na(ng lu+o+.ng ba(`ng kho^ng.
Ca'i na`y thi` sao ma` chu+'ng minh ddu+o+.c quan sa't tha^'y va^.y ma`.

  Tuy nhie^n co' the^? chu+'ng minh nhu+~ng me^.nh dde^` ye^'u ho+n:
Co' mo^.t ca'i ro`ng ro.c se~ dda.t ca^n ba(`ng khi the^' na(ng la` cu+.c 
tie^?u ne^'u kho^ng co' ai tho` tay va`o ke'o.

  Na(ng lu+o+ng ddu+o+.c ddi.nh nghi~a the^' na`o. OK, co' nhie^`u kie^?u 
ddi.nh nghi~a trong ca'c tru+o+`ng ho+.p cu. the^?. Dddi.nh nhi~a to^?ng 
qua't nha^'t la` trong termodynamics:
  Phie^'m ha`m trong kho^ng gian ca^'u hi`nh cu?a mo^.t he^. nhie^.t ddo^.ng
tho?a ma~n......
Va` he^. nhie^.t ddo^.ng thi` la` he^. thoa? ma~n ca'c tie^n dde^` co' no^.i 
dung ve^` ca'i phie^'m ha`m ddo'. Kie^?u lo`ng vo`ng nhu+ hi`nh ho.c mo+? 
dda^`u ba(`ng ddu+o+`ng tha(?ng va` ddie^?m ma` cha(?ng ai ddi.nh nghi~a ca?.
O^ng tha^`y tru+o=`ng la`ng cu?a to^i cu~ng thu+? ddinh nghi~a. Tuy 
nhie^n lo+'n le^n  to^i mo+'i hie^?u su+'c ma.nh cu?a tie^n dde^` la` o+? 
cho^~ ddu+o+`n tha(?ng co' the^? hie^? la` ddu+o+`ng cong, co`n ddie^?m 
co' the^? la` ca'i ba'nh ra'n to to^? bo^'. 

  Thu+.c cha^'t thi` he^. tie^n dde^` cu~ng la.i la` ddi.nh nghi~a mo^.t 
ddo^'ng kha'i nie^.m co+ so+? ma` tho^i.
 Na(ng lu+o+.ng va` ca^n ba(`ng cu~ng ddu+o+.c hi`nh thu+'c ho'a nhu+ va^.y.

Cheers
Aiviet