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The first law of thermodynamics at black hole horizons is known to beobtainable from the gravitational field equations. A recent study claims thatthe contributions at inner horizons should be considered in order to give theconventional first law of black hole thermodynamics. Following this method, werevisit the thermodynamic aspects of field equations in the Lovelock gravityand f(R) gravity by focusing on two typical classes of charged black holes inthe two theories.

Thermodynamic approach to field equations in Lovelock gravity and f(R) gravity revisited