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.

arXiv comment19 pages, 1 figure Version accepted in PRD. Few typos corrected and some references added

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Cited by in corpus (12)

• Thermodynamics of spacetime and unimodular gravity
• Modular Hamiltonian for de Sitter diamonds
• 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
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• New Approach to Unimodular Relativity
• Modular theory and affine representations on the Rindler horizon
• Thermodynamics of spacetime from minimal area