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 σₑₗ in unit of the transverse size L² of the wave packet, E₂ ~ σₑₗ/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 σₑₗ 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.
No takes yet. Share an insight, caveat, or question.
Low et al. (2024) studied this question.