A general derivation of the first law and Smarr formula for arbitrary generalized entropies yields a Ruppeiner curvature that vanishes exactly when the entropy obeys the Abé composition rule and diverges otherwise.
Ruppeiner, Springer Proc
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Exact ModMax black hole solution in higher-order gravity with quintessence yields analytical photon-sphere radius and shows dark energy and curvature corrections enlarge shadow size more than charge.
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Generalized First Law and Smarr Formula: Beyond Additivity and Extensivity
A general derivation of the first law and Smarr formula for arbitrary generalized entropies yields a Ruppeiner curvature that vanishes exactly when the entropy obeys the Abé composition rule and diverges otherwise.
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Thermodynamics and optical aspects of ModMax black holes in higher order curvature gravity with quintessence dark energy
Exact ModMax black hole solution in higher-order gravity with quintessence yields analytical photon-sphere radius and shows dark energy and curvature corrections enlarge shadow size more than charge.