  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.
