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In this paper, a preliminary correspondence between the thermodynamiccurvature and the isoperimetric theorem is established from a $4$-dimensionalultraspinning black hole. We find that the thermodynamic curvature ofultraspinning black hole is negative which means the ultraspinning black holeis likely to present an attractive between its molecules phenomenologically ifwe accept the analogical observation that the thermodynamic curvature reflectsthe interaction between molecules in a black hole system. Meanwhile we obtain ageneral conclusion that the thermodynamic curvature of the extreme black holeof the super-entropic black hole has a (positive or negative) remnantapproximately proportional to the reciprocal of entropy of the black hole.

The correspondence between thermodynamic curvature and isoperimetric theorem from ultraspinning black hole