Quantum Entropy Evolution

TL;DR

This paper investigates the time evolution of quantum coordinate-entropy in phase space, demonstrating its increase in certain scenarios and oscillations in entangled systems, with implications for particle creation and annihilation.

Contribution

It introduces the study of entropy evolution in quantum phase space, including entropy oscillations due to entanglement and the role of CPT symmetry in particle dynamics.

Findings

Entropy increases for coherent states under Dirac Hamiltonian.

Entropy oscillates during particle collisions due to spatial entanglement.

CPT with time translation links entropy decrease in particles to increase in antiparticles.

Abstract

A quantum coordinate-entropy formulated in quantum phase space has been recently proposed together with an entropy law that asserts that such entropy can not decrease over time. The coordinate-entropy is dimensionless, a relativistic scalar, and it is invariant under coordinate and CPT transformations. We study here the time evolution of this entropy. We show that the entropy associated with coherent states evolving under a Dirac Hamiltonian is increasing. However, for the collisions of two particles, where each is evolving as a coherent state, as they come closer to each other their spatial entanglement causes the total system's entropy to oscillate. We augment time reversal with time translation and show that CPT with time translation can transform particles with decreasing entropy for a finite time interval into anti-particles with increasing entropy for the same finite time interval. We then analyze the impact of the entropy law for the evolution scenarios described above and explore the possibility that entropy oscillations trigger the annihilation and the creation of particles.