Equilibrium to Einstein: Entanglement, Thermodynamics, and Gravity

Abstract

Here we develop the connection between thermodynamics, entanglement, and gravity. By attributing thermodynamics to timeslices of a causal diamond, we show that the Clausius relation $T\Delta S_{\text{rev}}=Q$, where $\Delta S_{\text{rev}}$ is the reversible entropy change, gives rise to the non-linear gravitational equations of motion for a wide class of diffeomorphism invariant theories. We then compare the Clausius relation to the first law of causal diamond mechanics (FLCD), a geometric identity and necessary ingredient in deriving Jacobson's entanglement equilibrium proposal -- the entanglement entropy of a spherical region with a fixed volume is maximal in vacuum. Specifically we show that the condition of fixed volume can be understood as subtracting the irreversible contribution to the thermodynamic entropy. This provides a "reversible thermodynamic process" interpretation of the FLCD, and that the condition of entanglement equilibrium may be regarded as equilibrium thermodynamics for which the Clausius relation holds. Finally, we extend the entanglement equilibrium proposal to the timelike stretched horizons of future lightcones, providing an entanglement interpretation of stretched lightcone thermodynamics.

23 pages, 2 figures

References in corpus (7)

• Towards a derivation of holographic entanglement entropy
• Entanglement equilibrium for higher order gravity
• The Holographic Shape of Entanglement and Einstein's Equations
• Gravitation and vacuum entanglement entropy
• Higher Curvature Gravity from Entanglement in Conformal Field Theories
• Einstein's Equations from the Stretched Future Light Cone
• Conformal Killing horizons and their thermodynamics

Cited by in corpus (16)

• Gravitational Thermodynamics of Causal Diamonds in (A)dS
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• New perspective on thermodynamics of spacetime: The emergence of unimodular gravity and the equivalence of entropies
• 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
• Modified Measures as an Effective Theory for Causal Fermion Systems
• Emergence of quadratic gravity from entanglement equilibrium
• From spacetime thermodynamics to Weyl transverse gravity
• The scalarized Raychaudhuri identity and its applications
• Gravity from thermodynamics in vacuum: Lorentz invariance and the role of Bel-Robinson tensor
• Gravity from equilibrium thermodynamics of stretched light cones
• Non-linear equation of motion for higher curvature semiclassical gravity
• Thermodynamics of spacetime from minimal area