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The recently proposed restricted phase space thermodynamics is shown to beapplicable to a large class of higher dimensional higher curvature gravitymodels coupled to Maxwell field, which are known as black hole scan models andare labeled by the spacetime dimension $d$ and the highest order $k$ of theLanczos-Lovelock densities appearing in the action. Three typical example caseswith $(d,k)=(5,1), (5,2)$ and $(6,2)$ are chosen as example cases and studiedin some detail. These cases are representatives of Einstein-Hilbert,Chern-Simons and Born-Infield like gravity models. Our study indicates that theEinstein-Hilbert and Born-Infield like gravity models have similarthermodynamic behaviors, e.g. the existence of isocharge $T-S$ phasetransitions with the same critical exponents, the existence of isovoltage $T-S$transitions and the Hawking-Page like transitions, and the similar hightemperature asymptotic behaviors for the isocharge heat capacities, etc.However, the Chern-Simons like $(5,2)$-model behaves quite differently. Neitherisocharge nor isovoltage $T-S$ transitions could occur and no Hawking-Page liketransition is allowed. This seems to indicate that the Einstein-Hilbert andBorn-Infield like models belong to the same universality class while theChern-Simons like models do not.

Restricted phase space thermodynamics for black holes in higher dimensions and higher curvature gravities