WestudythermodynamicsoftheparabolicLemaitre-Tolman-Bondi(LTB)cosmologysupportedbyaperfectSuidsource.ThismodelisthenaturalgeneralizationoftheSatFriedmann-Robertson-Walker(FRW)universe,anddescribesaninhomogeneousuniversewithsphericalsymmetry.AfterreviewingsomebasicequationsintheparabolicLTBcosmology,weobtainarelationforthedecelerationparameterinthismodel.Wealsoobtainaconditionforwhichtheuniverseundergoesanacceleratingphaseatthepresenttime.WeusethefirstlawofthermodynamicsontheapparenthorizontogetherwiththeEinsteinfieldequationstogetarelationfortheapparenthorizonentropyinLTBcosmology.WefindoutthatinLTBmodelofcosmology,theapparenthorizon’sentropycouldbefeededbyaterm,whichincorporatestheeffectsoftheinhomogeneity.Weconsiderthisresultandgetarelationforthetotalentropyevolution,whichisusedtoexaminethegeneralizedsecondlawofthermodynamicsforanacceleratinguniverse.WealsoverifythevalidityofthesecondlawandthegeneralizedsecondlawofthermodynamicsforauniversefilledwithsomekindsofmattersboundedbytheeventhorizonintheframeworkoftheparabolicLTBmodel.
