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In this paper, we consider higher order corrections of the entropy, whichcoming from thermal fluctuations, and find their effect on the thermodynamicsof higher dimensional charged black holes. Leading order thermal fluctuation islogarithmic term in the entropy while higher order correction is proportionalto the inverse of original entropy. We calculate some thermodynamics quantitiesand obtain the effect of logarithmic and higher order corrections of entropy onthem. Validity of the first law of thermodynamics investigated and Van derWaals equation of state of dual picture studied. We find that five-dimensionalblack hole behaves as Van der Waals, but higher dimensional case have not suchbehavior. We find that thermal fluctuations are important in stability of blackhole hence affect unstable/stable black hole phase transition.

Thermodynamics of higher dimensional black holes with higher order thermal fluctuations