Entropy Bound and Unitarity of Scattering Amplitudes

Understand

We establish that unitarity of scattering amplitudes imposes universal entropy bounds.

• The maximal entropy of a self-sustained quantum field object of radius R is equal to its surface area and at the same time to the inverse running coupling evaluated at the scale R.
• The saturation of these entropy bounds is in one-to-one correspondence with the non-perturbative saturation of unitarity by 2-to-N particle scattering amplitudes at the point of optimal truncation.
• These bounds are more stringent than Bekenstein's bound and in a consistent theory all three get saturated simultaneously.