Clausius Equation for Horizons in $F(R)$ Gravity

Abstract

Covariant Hamiltonian formulation of $F(R)$ gravity is used to find variation of surface Hamiltonian which leads to formulation of temperature and entropy of a horizon. These thermodynamic quantities are then used to establish an analogy between Einstein equation and Clausius equation. The obtained results are compared to those from classical General Relativity.