Symmetric and antisymmetric forms of the Pauli master equation (for interaction of matter and antimatter quantum states)

TL;DR

This paper introduces two forms of the Pauli master equation for matter and antimatter, demonstrating their thermodynamic implications and contrasting their predictions for matter-antimatter conversion.

Contribution

It proposes a time-antisymmetric form of the Pauli master equation and analyzes its thermodynamic consequences, extending the conventional symmetric form.

Findings

Symmetric PME predicts matter-antimatter equilibrium.

Antisymmetric PME favors antimatter conversion into matter.

Both forms are consistent with thermodynamic principles.

Abstract

When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter --- this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equi-balance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future.