Equipartition of Microscopic Degrees of Freedom, Space–time Entropy and Holography∗

One can identify the number density of the microscopic space–time degrees of freedom in any diffeomorphism-invariant theory of gravity by using the principle of equipartition, applied to the area elements of a surface ∂V which are at the local Unruh temperature. The entropy associated with these degrees of freedom, which matches with the Wald entropy for the theory, can be used to obtain the field equations of the theory through an extremization priciple. When the microscopic degrees of freedom are in local thermal equilibrium, the entropy of a bulk region of space–time resides on its boundary. These facts support an emergent perspective of gravity.