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

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

A. Alonso-Serrano; M. Liška

2020

Scholarcy highlights

  • The connection between thermodynamics and gravitational physics first appeared in the context of black hole thermodynamics
  • Building on the construction of Clausius entropy for bifurcating horizons, we present a novel derivation of Einstein equations from thermodynamics of local causal diamonds
  • By showing that this derivation is fully equivalent to the one based on maximal vacuum entanglement hypothesis, we showed that Clausius entropy and matter entanglement entropy can be used interchangeably in thermodynamics of spacetime in the semiclassical regime
  • For the case of conformal matter, we even explicitly prove the equivalence without appealing to gravitational physics in any way
  • Our method provides a connection between the maximal vacuum entanglement hypothesis approach and the original Jacobson’s thermodynamic derivation, as it reproduces the results obtained from MVEH in the same setting but using Clausius rather than matter entanglement entropy
  • We have employed the construction of Clausius entropy from previous research in the geometric setting of previous research, and we have found a result completely consistent with both approaches
  • We will address the issue of showing the entropy equivalence in a strict way for nonconformal matter and for generic local causal horizons

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