Abstract:
In thisthesis,weexplorethethermodynamiccharacteristicsofaBardeen
blackholethatinteractswithastringcloudandisminimallyconnectedto
nonlinear electrodynamics.Wepresentaentropyfunctionwith¯veparame-
ters, demonstratingitssingularity-freebehaviorthroughouttheentirecos-
mic evolutionoftheuniverse.Moreover,thisfunctionservestoextendthe
Tsallis, R¶enyi,andSharma-Mittalentropiesforappropriateparameterlimit
conditions.ForinstancetheTsallisentropyisexpressedas ST = S±, where
± representstheTsallisexponentand S denotes theBekenstein-Hawking
entropy.Thisformulaisparticularlyapplicabletosystemswithlong-range
interactionswheretheBoltzmann-Gibbsentropyisnotsuitable.It'sevident
that when ± = 1,theTsallisentropyconvergestotheBekensteinHawking
limit, butforvaluesof ± other than1,itdoesnotexhibitadditivity.On
the contrary,theR¶enyientropyitconvergestotheBekenstein-Hawking
limit asaapproacheszero.WhiletheTsallisandR¶enyientropiesmightbe
combinedtogeneratetheSharma-Mittalentropy,theR¶enyientropywas
¯rst o®eredasawaytoassessinformationcontent.Weanalyzeavariety
of parameters,includingmass,temperature,pressure,andGibbsfreeen-
ergy,usingtheTsallis,R¶enyi,andSharma-Mittalentropies.Inourstudy,
wederivestablebehaviorand¯ndphysicalsolutionsbytakingparticular
valuesfortheparameters a and q.
