Simple sufficient conditions for the generalized covariant entropy bound

TL;DR

This paper derives the generalized covariant entropy bound and the generalized Bekenstein bound from simple, phenomenological assumptions about entropy currents, providing clearer conditions under which these bounds hold.

Contribution

It presents a simplified derivation of key entropy bounds using minimal assumptions, clarifying their applicability in various regimes.

Findings

Both bounds can be derived from bounded entropy current gradients.

The assumptions apply broadly despite intrinsic limitations of local entropy descriptions.

The derivation simplifies previous frameworks, enhancing transparency.

Abstract

The generalized covariant entropy bound is the conjecture that the entropy of the matter present on any non-expanding null hypersurface L will not exceed the difference between the areas, in Planck units, of the initial and final spatial 2-surfaces bounding L. The generalized Bekenstein bound is a special case which states that the entropy of a weakly gravitating isolated matter system will not exceed the product of its mass and its width. Here we show that both bounds can be derived directly from the following phenomenological assumptions: that entropy can be computed by integrating an entropy current which vanishes on the initial boundary and whose gradient is bounded by the energy density. Though we note that any local description of entropy has intrinsic limitations, we argue that our assumptions apply in a wide regime. We closely follow the framework of an earlier derivation, but our assumptions take a simpler form, making their validity more transparent in some examples.