
theel soochika

vamseeya verthiriv alakkaanum ithu upayogichittundengilum saambathika asamathvavum mattu saambathika prathibhaasangalum alakkaan praadhamikamaayi upayogikkunna oru sthithivivarakkanakkaanu theel soochika.
vivara sidhaanthathile redendensic thulyamaanu theel soochika 'tii' tii, ithu daattayude paramavadhi entropyaanu mainus nireekshicha entropy. ithu saamaanyavalkkaricha entropy soochikayude oru prathyeka kesaanu. aavarthanam, vaividhyathinte abhavam, ottappedal, verthirikkal, asamathvam, kramarahitata, compressibility ennivayude alavukol aayi ithine kaananakum. irasmus yooniversitti rotterdamile oru dutch saambathika vidagthanaaya henry theel (1924-2000) aanu ithu nirddeshichathu.
henry theel thanne (1967) paranju "janasamkhyayude vihithathe munkoor saadhyathakalaayi parivartthanam cheiyunna paroksha sandeshathinte prathekshikkunna vivara ulladakkamaayi (theel) soochikaye vyaakhyaanikkaam."
amartya seen abhiprayappettu, "ennaal theel soochika oru ekapaksheeyamaaya soothravaakyamaanu, varumanam kondu bharamullah varumaana oharikalude parasparangalude logaritham sharashari avabodhajanyamaaya ardhathil krithyamaayi ozhukunna oru alavukol allah."
formula.
x" enna swabhaavamulla oro "n" ejantumaarudeyum janasamkhyaykku, saahacharyathe "x" i "(" i "= 1) enna listt prathinidheekarikkam.., n") ivide "x" i "ennathu ejantu" i "yude swabhaavamaanu. udaaharanathinu, varumaanamaan savisheshathayenkil, "xi" ennathu ejantinte "i" yude varumaanamaan.
theel "tii" soochikaye ingane nirvachichirikkunnu
koodaathe theel "ell" soochikaye ingane nirvachichirikkunnu
ivide formula _ 3 aanu sharashari varumanam
paramavadhi entropyumaayi (paramavadhi entropy) bandhappett alakkunna oru vyakthiyude varumaana-vitharanathinte diss-entropyaanu theel-ell...ithu poornna samathvathode nedunnu).
valia varumaanavum cheria varumaanavum thammilulla kaimaattam valia varumaana anupaathathe maattunnathinekkaal cheria varumaana anupaathathe mattumennathinaal, kaimatta-thathwam eee soochika thripthippeduthunnu.
thulyamaayi, sahacharyam oru vyathiriktha vitharana function "f" k "(" k "= 0..," "" ")" "" "k" "varumaanamulla janasamkhyayude bhinnasankhyayaaya" "f" "k" umm "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "" "
ivide formula _ 3 veendum sharashari varumaanamaan
eee saahacharyathil varumanam "k" oru poornnasamkhyayaanennum "k = 1" saadhyamaaya ettavum cheria varumaana vardhanavine prathinidheekarikkunnuvennu shradhikkuka (udha.jii., sents).
f" ("k") "dk" ennathu "k" muthal "k" + "dk" vareyulla varumaanamulla janasamkhyayude bhinnasankhyayaaya oru thudarchayaaya vitharana functionaaya "f" ("k") (0 muthal anantatha vare pinthunaykkunnu) eee saahacharyathinte savisheshatha aanenkil, appol theel soochika iprakaaramaanu
evideyaanu sharashari
chila saadhaarana thudarchayaaya probability vitharanagalkkulla theel soochikakal chuvadeyulla pattikayil nalkiyirikkunnu
ellaavarkkum ore varumaanamundengil, "t" t ennathu 0 nuu thulyamaanu. oru vyakthikk ellah varumaanavum undengil, "t" t ennathu phala soothravaakyam nalkunnu, athu paramavadhi asamathvamaanu. t" t-neey formula _ 11 kondu harikkunnathiloode samavaakyathe 0 muthal 1 vare saadhaarana nilayilakkaan kazhiyum, ennaal thudarnnu swaathanthrya soothravaakyam lamghikkappedunnu formula _ 13 asamathvathinte alavukol aayi yogyamalla.
ore varumaanamulla ellaavarudeyum samathvaavasthayil ninnu akaleyulla janasamkhyayude oru entropic "dooram" theel soochika alakkunnu. samkhyaaparamaaya phalam negatteevu entropy adisthaanathilaanu, athinaal uyarnna samkhya poornna samathvathil ninnu kooduthal akaleyulla kooduthal kramatthe soochippikkunnu. entropic pakaram negatteevu entropy prathinidheekarikkunnathin soochika roopappeduthunnathu samathvathekkaal asamathvathinte alavukolakkaan anuvadikkunnu.
atkinsan soochikayumaayulla bandham.
theel soochikaye 0 num 1 num (0 sathamaanavum 100%) edayilulla oru atkinsan soochikayaayi parivartthanam cheyyaan kazhiyum, ivide 0 thikanja samathwatheyum 1 (100%) paramavadhi asamathvatheyum soochippikkunnu. (parivarthanatthinaayi saamaanyavalkkaricha entropy soochika kaanuka.)
entropyil ninnulla vyulppannam.
shaannante vivara entropy formula _ 14 ll ninnaan theel soochika uruthirinjathu, ivide entropy ennathu oru nischitha koottam vivarangalile kramarahithathayude alavaanu. vivara sidhaantham, bhauthikashaasthram, theel soochika ennivayil entropy pothuvaaya roopam
oru janasamkhyayile varumaanathinte vitharanam nokkumbol, formula 17 ennathu oru prathyeka vyakthiyude varumaanavum muzhuvan janasamkhyayudeyum motham varumaanavum thammilulla anupaathathinu thulyamaanu. ithu oru janasamkhyayude nireekshicha entropy soothravaakyam _ 23 ingane nalkunnu
nireekshicha entropy (formula _ 23, ithu kramarahithamaya varumanam engane vitharanam cheyyappedunnu ennathine prathinidheekarikkunnu) saadhyamaaya ettavum uyarnna entropyil ninnu ethratholam varunnuvennu theel soochika formula _ 32 alakkunnu (formula _ 34, janasamkhyayile vyakthikalkkidayil varumanam paramavadhi vitharanam cheiyunnathine prathinidheekarikkunnu-ananthamaaya ennam kramarahithamaya nanayangal eriyunnathinte phalathinu samanamaaya oru vitharanam thalakaludeyum vaalukaludeyum thulya vitharanam). athinaal, nireekshicha entropy mainus cheiyunna saidhaanthika paramavadhi entropy (oro vyakthiyudeyum varumanam thulyamaanengil athu kaivarikkum) thammilulla vyathyaasamaan theel soochika.
formula _ 30 janasamkhya/speesheesukalude yoonittukalilaayirikkum, formula _ 23 ennathu jaivavaividhyathinte alavaanu, ithine shaanon soochika ennu vilikkunnu. theel soochika x = janasamkhya/speesheesukal ennivaykkoppam upayogikkukayaanenkil, athu oru koottam speesheesukal thammilulla janasamkhyayude asamathvathinte alavukolaanu, allengil "sambathu ottappedalinu" pakaram "bio-isolation" aanu.
vivara sidhaanthathil redendency ennu vilikkappedunnathaanu theel soochika alakkunnathu. vivarangal kaimaran upayogikkaatha "information space" aanu vila signalinte falaprapti kuraykkunnathu. chila vyakthikalil varumaanathinte (allengil sambathinte mattu alavukal) aavarthanathinte alavaanu theel soochika. chila vyakthikalil aavarthanasheshi mattullavaril kuravine soochippikkunnu. oru amarthappedaatha tekst fayalinu labhyamaya advitheeya baitt pratheekangalkk thulyamaaya ennam baitt lokkeshanukal illaathathupole motham varumanam vyakthikalkkidayil thulyamaayi vitharanam cheythittillenn uyarnna theel soochika soochippikkunnu. 
vighadippikkal.
lokabaankinte abhipraayathil, "ettavum ariyappedunna entropy alavukal theels tii (formula _ 32), theels ell (formula _ 39) ennivayaanu, iva randum asamathvathe pradeshangalkkullile asamathvam moolamulla bhaagathekku vighadippikkaan anuvadikkunnu (udha.jii. nagara, grameena) pradeshangal thammilulla vyathyaasangal moolamulla bhaagavum (udha.jii. grameena-nagara varumaana vidavu). saadhaaranayaayi oru raajyathe asamathvathinte naalil moonnu bhaagamenkilum grouppinullile asamathvavum backie paadam grouppukal thammilulla vyathyaasavumaan."
janasamkhyaye formula _ 40 upavibhagangalaayi vibhajikkukayaanenkil 
appol theels tii soochika
udaaharanathinu, yunaittad stetsinullile asamathvam oro samsthaanathinakathum samsthaana varumaanavum samsthaanangal thammilulla asamathvavum adisthaanamaakkiyulla sharashari asamathvamaanu.
asamathvathinte speshyal maanatthinte aapekshika praadhaanyam soochippikkunnathinaal, pradeshathinumidayilulla gadakathinu kaaranamakunna vihitam thirichariyunna theel soochikayude vighadanam praadeshika asamathvathinte kriyaathmaka vishakalanathin sahayakaramaaya upakaranamaayi maarunnu.
theelinte 'tii' yum theelinte 'ell' umm thammil.
theelinte 'tii' yum theelinte 'ell' umm vighadippikkaavunnavayaanu. avaa thammilulla vyathyasam oronnum upayogikkunna phala vitharanathinte bhaagathe adisthaanamaakkiyullathaanu. pothuvalkkaricha entropy (ge) kudumbatthile asamathvathinte soochikakal ge soochikaye nirvachikkunna oru maanadandatthe aashrayich paavappettavarkkidayilo sambannarkkidayilo varumaana vihithathile vyathyaasangalodu kooduthal sensitiivu aanu. jiiyude paaraameettar moolyam cheruthaanenkil, vitharanathinte thaazheyulla vyathyaasangalodu athu kooduthal sensitiivu aanu.
kooduthal janapriyamaaya jini coffificient nalkaatha theel soochikayude oru savisheshathayaanu decomposibility. laurence vakrathe adisthaanamaakkiyullathinaal jini coffificient palarkkum kooduthal avabodhajanyamaan. ennirunnaalum, ithu theel pole eluppathil vighadippikkaanaavilla.
aaplikkeshanukal.
niravadhi saambathika prayogangalkku purame, jalasechana samvidaanangalude prakadanavum software alavukalude vitharanavum vilayiruthunnathin theel soochika prayogichittundu.

