New perspective on thermodynamics of spacetime: The emergence of unimodular gravity and the equivalence of entropies

Abstract

We present a novel derivation of Einstein equations from the balance between Clausius entropy crossing the boundary of a local causal diamond and entanglement entropy associated with its horizon. Comparing this derivation with the entanglement equilibrium approach developed by Jacobson, we are able to argue for the equivalence of matter entanglement and Clausius entropy in the semiclassical regime. We also provide a direct comparison of both entropies for conformal matter, showing their equivalence without appealing to gravitational dynamics. Furthermore, we determine that gravitational dynamics implied by thermodynamics of spacetime, in fact, corresponds to unimodular gravity rather than general relativity.

19 pages, 1 figure Version accepted in PRD. Few typos corrected and some references added

References in corpus (4)

• Entanglement equilibrium for higher order gravity
• Unruh-DeWitt detector event rate for trajectories with time-dependent acceleration
• Conformal quantum mechanics of causal diamonds
• Thermodynamics of Spacetime and Unimodular Relativity

Cited by in corpus (12)

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• Noether charge formalism for Weyl invariant theories of gravity
• Noether charge formalism for Weyl transverse gravity
• Thermodynamics as a tool for (quantum) gravitational dynamics
• Emergence of quadratic gravity from entanglement equilibrium
• From spacetime thermodynamics to Weyl transverse gravity
• Quantum black holes as classical space factories
• Gravity from thermodynamics in vacuum: Lorentz invariance and the role of Bel-Robinson tensor
• New Approach to Unimodular Relativity
• Modular theory and affine representations on the Rindler horizon
• Thermodynamics of spacetime from minimal area