A Causal Entropy Bound

The identification of a causal-connection scale motivates us to propose a new covariant bound on entropy within a generic space-like region. This “causal entropy bound”, scaling as √ EV , and thus lying around the geometric mean of Bekenstein’s S/ER and holographic S/A bounds, is checked in various “critical” situations. In the case of limited gravity, Bekenstein’s bound is the strongest while naive holography is the weakest. In the case of strong gravity, our bound and Bousso’s holographic bound are stronger than Bekenstein’s, while naive holography is too tight, and hence typically wrong. The second law of thermodynamics states that the entropy of a closed system tends to grow towards its largest possible value. But what is this maximal value? Bekenstein [1] has suggested that, for a limited gravity system of energy E, whose size R is larger than its gravitational radius, R > Rg ≡ 2GNE, entropy is bounded by SBEB, SBEB = ER/h̄ = Rg R l −2 P , (1)