Clausius entropy for arbitrary bifurcate null surfaces

Abstract

Jacobson's thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson's original article, this more general construction sharply brings into focus the questions: Is entropy objectively "real"? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora's box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation dS = dQ/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces --- effectively defining a "virtual Clausius entropy" for arbitrary "virtual (local) causal horizons". As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition (NEC). Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson's derivation of the Einstein equations.

19 pages, 5 figures. V2: Seven references added; minor edits. V3: Now 24 pages, 7 figures. Significant revision and extension of the presentation, but technical calculation largely unchanged. Some 25 references added. This version accepted for publication in Classical and Quantum Gravity

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Cited by in corpus (11)

• New perspective on thermodynamics of spacetime: The emergence of unimodular gravity and the equivalence of entropies
• Thermodynamics of spacetime and unimodular gravity
• Covariant approach to the thermodynamic structure of a generic null surface
• Entropy bounds and field equations
• Thermodynamics as a tool for (quantum) gravitational dynamics
• Einstein's equations and the pseudo-entropy of pseudo-Riemannian information manifolds
• Emergence of quadratic gravity from entanglement equilibrium
• From spacetime thermodynamics to Weyl transverse gravity
• From mindless mathematics to thinking meat?
• Gravity from thermodynamics in vacuum: Lorentz invariance and the role of Bel-Robinson tensor
• Gravity from equilibrium thermodynamics of stretched light cones