In ordinary QM and QFT entropy is defined using a density operator for a generalized state:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]S = -\text{tr}\left(\rho\,\ln\rho\right)[/tex]

b/c for the gravitational field we do neither know the fundamental degrees of freedom nor the Hilbert space states, a definition like

[tex]\rho = \sum_np_n\,|n\rangle\langle n|[/tex]

is not available.

Questions:

1) are there attempts to formulate entropy for a QFT on a gravitational background for a "finite volume"?

2) are there attempts to formulate entropy for the gravitational field "within this finite volume"?

3) has this been done in string theory and / or spin networks for several different spacetimes (black holes, some other finite volume, expanding spacetime with e.g. co-moving dust, ...)?

4) how does the holographic principle show up?

(I know some special cases like the state counting for black holes in LQG, but I have never seen a general construction)

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# Gravitational entropy

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