".
by Jaynes was also kind of interesting as well. In one part he talks about how entropy is only defined up to an abitrary function of particle number $N$ in "phenomenological thermodynamics".

A:

There is no need for quantum mechanics. You can find a classical argument in Landau-Lifshitz, Statistical Physics, Chapter III, Paragraph 31.
What you have to understand is that when integrating over phase space, for example to calculate the free energy in the canonical ensemble, you should not integrate over all values of the canonical variables $p,q$, but only over the values which correspond to different physical states. Landau uses the notation $\int'$ to denote this; for example for the free energy you will have
$$\beta F = -  \ln \int' e^{-\beta \mathcal H(p,q)} dp dq$$ 
where $\beta=1/k_B T$ as usual. 
Now, it is often more practical to just integrate over the whole phase, i.e. to take $\int dp dq$ space instead that over the portions of phase space corresponding to different states, i.e. $\int' dp dq$. 
However, if you do so, you are overcounting the number of states. In the case of a gas of $N$ atoms, in order to get the correct counting, you have to divide the integral extended over the whole phase space by the number of possible permutations of $N$ atoms, which is $N!$. This is because if you switch the position of two identical atoms you are not getting a new physical state (this is the key point of the whole argument). To sum up, for a gas of $N$ identical atoms we have
$$\int'\dots dp dq = \frac 1 {N!} \int \dots dp dq$$
which is Eq. 31.7 in my edition of Landau-Lifshits.

 Q:

Ajax based username availablity checking and then generating some username to use in jsp

i have somewhat done a ajax based jsp coding for checking username availability. It worked perfectly. Though it might have some errors. So if there any please point it out. Now my main question is that after the checking i also want generate some usernames for users to use like we can see it at gmail registration form. I am giving my code here...
First the
". 
 by Jaynes was also kind of interesting as well. In one part he talks about how information is merely defined up to an abitrary function of particle phone number $ N$ in " phenomenological thermodynamics ". 

 A: 

 There is no indigence for quantum machinist. You can find a classical argument in Landau - Lifshitz, Statistical Physics, Chapter III, Paragraph 31. 
 What you have to understand is that when integrate over phase space, for example to forecast the spare energy in the canonical ensemble, you should not integrate over all values of the canonic variables $ p, q$, but only over the value which correspond to different physical states. Landau use the notation $ \int'$ to denote this; for example for the free energy you will own 
 $ $ \beta F = -   \ln \int' e^{-\beta \mathcal H(p, q) } dp dq$$ 
 where $ \beta=1 / k_B T$ as usual. 
 Now, it is often more practical to barely integrate over the whole phase, i.e. to take $ \int dp dq$ space instead that over the portions of phase space corresponding to different states, i.e. $ \int' displaced person dq$. 
 However, if you make so, you are overcounting the issue of state. In the case of a gas of $ N$ atoms, in orderliness to have the correct counting, you accept to divide the integral extended over the whole phase space by the number of potential permutations of $ N$ atoms, which is $ N!$. This is because if you switch the position of two identical atoms you are not getting a new forcible department of state (this is the key point of the whole argument). To summarize up, for a gas of $ N$ identical atoms we have 
 $ $ \int'\dots displaced person dq = \frac 1 { N! } \int \dots dp dq$$ 
 which is Eq. 31.7 in my version of Landau - Lifshits. 

  Q: 

 Ajax based username availablity checking and then generating some username to use in jsp 

 i have somewhat done a ajax base jsp coding for checking username handiness. It worked perfectly. Though it might have some errors. thus if there any please point it out. immediately my main question is that after the checking i also want generate some usernames for user to use like we can go steady it at gmail registration form. I am giving my code here... 
 First the
".
by Uaynes was also kind of lnteresting as wglo. In oie part he talkr about how entropy is only vefibed uk to an abitrary fuvction of particlw nunver $N$ in "pisnomenologicam thexmidynamics".

A:

Therg is no need for quantum macfauics. You can find a classical argumegt in Lsnfau-Lifshitz, Stwtisuicwl Pgjslcs, Chapter III, Paragraph 31.
What yku have to understanc is that when integrating oveg phase space, for fxample to xalctoate the fred energy in the canonidal ensemble, you should not intdgratz over all caoued of the caninicaj variables $i,a$, but mnly ovrr the values ehirh cirrespond to differenv physical states. Lagdau uses tke notation $\int'$ to debore thhs; fmr ebqmpue roc tge fref eiergy you wjll have
$$\betq F = -  \ln \int' e^{-\beta \mwnncal H(p,q)} dp sq$$ 
whewe $\beta=1/k_B T$ as usual. 
Now, it is often more przctical to just integrare over the whole phade, i.e. to eake $\int dp dq$ space instead that over the portiots of ohawe rpafe corresponding to different states, i.e. $\int' d[ da$. 
Mowever, if you dj so, you arr lvrtcounting the vumber of states. In the casf of a das od $N$ atoms, in prder to get the correct coynting, you hcve to divide the intzgral extendzd ovet the ehole phase space by thz numbsr of possihle permufxtions of $N$ atomr, wmicv is $N!$. This is because if rou switci the positiun og two ydentical wtoms you are not gettinh a ngw phyvical statf (this is the key point of the xiole argument). Tm slm up, for a gax of $N$ identisal atoms we hcve
$$\int'\docs dp aq = \frac 1 {H!} \int \dmts dp dq$$
whych is Eq. 31.7 in ly edition oh Landau-Lyfshuts.

 W:

Ajax bxred username afailablitj ehecking qnd then generatinn somg hsername to use in jsp

i have someehag djnv a atdx based jsp codkng gor cfecking usevnaoe afailability. It workeg pedfectly. Though it kinht have wome errjrs. So if thete any please poinu it ont. Now my msin question is that after the chscking i wlsj want generwte wome usernamzs for users to use like we can see it av gmail registration foem. I am giving my cpce here...
Firsv the
". by Jaynes was also kind of well. one part talks about how to abitrary function of number $N$ in thermodynamics". A: There is no need quantum mechanics. You can find a classical argument in Landau-Lifshitz, Statistical Physics, Chapter Paragraph 31. What you have to understand is that when integrating over phase for to the energy in the canonical ensemble, you should not integrate over all values of the canonical variables but only over the values which correspond to physical states. Landau uses notation $\int'$ to denote this; example the free you have F = - \int' e^{-\beta \mathcal H(p,q)} dp dq$$ where $\beta=1/k_B T$ as usual. Now, it is often more practical just integrate whole phase, to $\int dq$ space instead the portions of phase space corresponding i.e. $\int' dp dq$. However, if you do you are the number of states. In the of a gas of $N$ atoms, in order get the correct counting, you have to divide the integral extended over the whole phase the number of possible of $N$ atoms, is This because you switch position of two identical atoms you are not getting a new state (this is the key point of the whole argument). up, a gas of identical atoms we have dp = \frac 1 {N!} dp which in edition Landau-Lifshits. Q: Ajax based availablity checking and then generating username to use in a ajax based jsp coding for checking username It worked perfectly. Though it might have errors. So if there any please point it out. Now my main is that checking i also want generate some usernames for to use like we see it at gmail registration form. I am giving code First the
".
by Jaynes was also kind of inteResting as wEll. In One ParT hE talKs abOut how entropy iS Only Defined up to an abitrary fUnctiOn OF parTIcLe numBer $N$ in "pHEnOMEnoLoGiCal ThERmOdynaMicS".

A:

There Is no need foR quAnTum mechanics. yOu Can find a clAssIcal argument In LAndau-LIfShiTZ, StatIstIcal PHysics, cHapter iII, ParagrApH 31.
what yoU Have to uNDErStanD is that when integrATiNG over phase spacE, for exAmPLe TO CalCulAte the free EnErgy iN The canoNIcAL ENseMBle, you should nOt integrate OVer All valUeS of THe canoNical VaRIabLes $p,q$, but onlY oveR the valueS which COrrespoND to diffErent pHysIcaL staTEs. laNdaU uSEs tHE nOtaTIon $\Int'$ to denOtE tHis; foR exaMPLE For tHe fRee eNergy You will have
$$\beTa F = -  \Ln \inT' E^{-\beTa \matHcal H(P,q)} dp Dq$$ 
Where $\Beta=1/k_B t$ as usUaL. 
Now, it is often moRe prActical to JusT iNteGrAte ovER the whOle PhaSe, i.e. to tAke $\int dP Dq$ sPaCE INsTead that over the porTiONS oF phase spAce corREsPoNDing to diFfEreNt stATEs, i.e. $\iNt' dp DQ$. 
HOwever, if You do sO, YoU aRe overcOuNting tHe NumBer Of staTEs. In The casE of a gas oF $N$ atoMS, in order to get tHE correct countINg, YOU hAVe to DivIde the integRal eXTendEd ovER tHe wHOle phAse spAcE By THe number of possible pErMutatiOns of $n$ atoms, which is $n!$. This is becAUSE if you swItch THe POsition of two idEnticAl atoms you ARe not getTing a New physiCal state (tHIS is the keY poInt Of tHe wHOLe Argument). To sum UP, For a GaS of $N$ ideNtiCal atomS we HavE
$$\inT'\doTs Dp dq = \frac 1 {N!} \Int \dots dP dQ$$
wHiCh Is EQ. 31.7 in my EDition of laNdaU-LIfsHits.

 Q:

aJax basEd useRnamE aVaILabLity cheCKiNG And tHeN gEnerAtiNg Some uSernAMe tO use in jSp

i have soMewHAt doNe A aJax baseD jsp coding for ChEcking userNaMe aVailabILIty. It worKed perfectly. Though it migHT have soMe eRrors. so if There any pLeaSe poinT it OUt. Now mY main qUestiOn Is tHAT afteR THe CheCkIng i also waNT GenErate SoMe usErnames For users to use like wE Can See it at gmail rEgiStraTIOn ForM. i aM GivInG My cODE here...
First the
".
by Jaynes was also kind  of intere sting  as  we ll . In  one  part he talks abou t how entropy is onlydefin ed up t o  a n abi trary f u nc t i onof  p art ic l enumbe r $ N$ in " phenomenol ogi ca l thermodyna m ic s".

A:

T her e is no need  fo r quan tu m m e chani cs.  Youcan fi n d a cl assical a rg u ment i n  Landau - L if shit z, Statistical Ph y si c s, Chapter III , Para gr a ph 3 1.Wha t you have  t o und e rstandi st h a t w h en integratin g over phas e  sp ace, f or  ex a mple t o cal cu l ate  the free e nerg y in thecanoni c al ense m ble, yo u shou ldnot  int e gr at e o ve r  al l  v alu e s o f the ca no ni cal v aria b l e s  $p, q$,  but  only  over the val ues  whi c h c orres pondto d if feren t phys icalst ates. Landau us es t he notati on$\ int '$  to d e note t his ; f or exam ple for the  f r e e  e nergy you will hav e$ $ \b eta F =-  \ln \i nt '  e^{-\be ta  \m athc a l  H(p, q)}d pdq$$ 
wh ere $\ b et a= 1/k_B T $as usu al . Now , iti s of ten mo re pract icalt o just integra t e over the wh o le p ha s e, i .e.  to take $\ intd p dq $ sp a ce  in s teadthatov e rt he portions of phas espacecorre sponding to d ifferent s t a t es, i.e.  $\i n t' dp dq$. 
Howev er, i f you do s o , you ar e ove rcountin g the num b e r of sta tes . I n t hec a se  of a gas of$ N $ at om s, in o rde r to ge t t hecor rec tcounting,  you hav eto  d iv ide  thei ntegralex ten de d o ver t h e whol e pha se s pa ce bythe num b er o f po ss ib le p erm ut ation s of $N$  atoms,  which is  $N ! $. T hi sis beca use if you sw it ch the pos it ion  of tw o identica l atoms you are not get t ing a n ewphysi calstate (th isis the  ke y  point  of th e who le  ar g u ment) . To  su mup, for ag a s o f $N$  i dent ical at oms we have
$$\int ' \do ts dp dq = \f rac  1 { N ! }\in t  \ d ots  d p  dq $ $ 
which is Eq. 3 1.7 in myed i ti on of Land a u-L if shits.
 Q:

A jax b a sed use rname ava ilablitych ecki n g  an d then gen eratingsome user n ame t o  u se in  js p

i h av e s omewh at don e  aajaxbasedjs p codi ng fo rchecking  username availability.  It wo rkedper fectly. T hou g h i t might h avesome error s.Soif th ere any p leas e  p oin t  it o ut.N ow my mai n  q ues t i on  is that af t e r  th e che cki n g i al so w ant generate some usernames foruser s touse like  w e can see it a t g ma i l  registr at ion form. I  am givi ng my co de her e...
F irst th e 
".
by Jaynes_was also_kind of interesting as_well. In_one_part he_talks_about how entropy_is only defined_up to an abitrary_function of particle_number_$N$ in "phenomenological thermodynamics".

A:

There is no need for quantum mechanics. You can find a_classical_argument in_Landau-Lifshitz,_Statistical_Physics, Chapter III, Paragraph 31.
What_you have to understand is_that when_integrating over phase space, for example to calculate_the_free energy in_the canonical ensemble, you should not integrate over all_values of the canonical variables $p,q$,_but only over_the_values_which correspond to different_physical states. Landau uses the notation_$\int'$ to denote this; for example_for the free energy you will have
$$\beta_F = -  \ln \int'_e^{-\beta \mathcal H(p,q)} dp dq$$_
where $\beta=1/k_B_T$ as usual. 
Now, it_is often more_practical to_just integrate over_the whole phase, i.e. to take_$\int dp dq$_space instead that over the portions_of_phase space corresponding_to_different_states, i.e._$\int' dp dq$._
However,_if you_do_so, you are overcounting the number_of_states. In the case of a gas_of $N$ atoms, in_order_to get the correct_counting, you have to divide_the integral extended over the whole_phase space_by the_number of possible permutations of $N$ atoms, which is $N!$. This_is because if you switch the_position of two identical_atoms you_are_not getting a_new_physical state_(this is the key point of the_whole argument)._To sum up, for a gas_of $N$ identical atoms_we_have
$$\int'\dots dp dq = \frac 1_{N!} \int \dots dp dq$$
which is_Eq. 31.7 in my edition_of_Landau-Lifshits.

_Q:

Ajax based username availablity checking_and then generating some username to_use in jsp

i_have somewhat done a ajax based jsp_coding_for checking username availability. It worked_perfectly._Though it might have some errors._So_if_there any please point it_out. Now my main question is_that after the checking i also want generate some_usernames for users_to use like we can_see_it_at gmail registration form. I am giving my code here...
First_the