Abstract
The scattering cross section is the effective area of collision when two particles collide. Quantum mechanically, it is a measure of the probability for a specific process to take place. Employing wave packets to describe the scattering process, we compute the entanglement entropy in 2-to-2 scattering of particles in a general setting using the S-matrix formalism. Applying the optical theorem, we show that the linear entropy E₂ is given by the elastic cross section σ_el in unit of the transverse size L² of the wave packet, E₂ ∼ σ_el/L², when the initial states are not entangled. The result allows for dual interpretations of the entanglement entropy as an area and as a probability. Since σ_el is generally believed, and observed experimentally, to grow with the collision energy √s in the high energy regime, the result suggests a "second law" of entanglement entropy for high energy collisions. Furthermore, the Froissart bound places an upper limit on the entropy growth.