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

A. Y. Klimenko|arXiv (Cornell University)|Nov 12, 2016

Cold Atom Physics and Bose-Einstein Condensates13 references4 citations

TL;DR

This paper introduces an antisymmetric form of the Pauli master equation (APME) that, unlike the conventional symmetric form (SPME), predicts full conversion of antimatter into matter by assigning opposite thermodynamic time directions to matter and antimatter. The APME is derived from unitary quantum mechanics with decoherence assumptions, and its validity is confirmed via a new H-theorem, demonstrating consistency with CPT-invariant thermodynamics and offering a framework to test antimatter's thermodynamic behavior experimentally in the future.

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.

Motivation & Objective

• To explore the possibility of extending thermodynamics from matter to antimatter through symmetric and antisymmetric formulations.
• To derive a time-antisymmetric version of the Pauli master equation (APME) consistent with thermodynamic time reversal between matter and antimatter.
• To establish the validity of the H-theorem for both symmetric and antisymmetric forms, ensuring entropy increase and thermodynamic consistency.
• To investigate whether the antisymmetric PME favors matter-antimatter conversion, particularly full conversion of antimatter into matter.
• To clarify the implications of CPT invariance in thermodynamic behavior when applied to antimatter, especially in the absence of experimental data.

Proposed method

• Derives the antisymmetric Pauli master equation (APME) from unitary quantum mechanics by assuming decoherence occurs before interactions, not after, to break time symmetry.
• Applies the Stosszahlansatz-like hypothesis (molecular chaos) to define the direction of thermodynamic time in the APME, distinguishing it from the symmetric version.
• Proves a new H-theorem for the APME, demonstrating monotonic entropy increase under the antisymmetric time convention.
• Compares the symmetric (SPME) and antisymmetric (APME) forms in terms of their predictions for matter-antimatter state probabilities and evolution.
• Analyzes the implications of CPT invariance in the context of thermodynamic time, showing that the antisymmetric form preserves CPT symmetry under specific conditions.
• Considers the role of environmental and intrinsic decoherence in shaping thermodynamic behavior, particularly in macroscopic antimatter systems.

Experimental results

Research questions

• RQ1 Can the Pauli master equation be formulated in a time-antisymmetric form that assigns opposite thermodynamic time directions to matter and antimatter?
• RQ2 Does the antisymmetric form of the PME predict a preference for antimatter-to-matter conversion over equi-balance?
• RQ3 Is the antisymmetric PME consistent with the second law of thermodynamics, as demonstrated by a valid H-theorem?
• RQ4 How does CPT invariance relate to the symmetric and antisymmetric extensions of thermodynamics for antimatter?
• RQ5 What experimental conditions would be required to distinguish between symmetric and antisymmetric thermodynamic behavior in antimatter?

Key findings

• The antisymmetric form of the Pauli master equation (APME) predicts full conversion of antimatter into matter, in contrast to the symmetric form, which predicts equi-balance between matter and antimatter states.
• The APME satisfies a new H-theorem, proving monotonic entropy increase under the antisymmetric time convention, thus ensuring thermodynamic consistency.
• The symmetric and antisymmetric versions of the PME correspond to symmetric and antisymmetric extensions of thermodynamics, respectively, with the antisymmetric version being CPT-invariant under the conditions specified in Proposition 1.
• The derivation of APME relies on a time-asymmetric decoherence assumption—decoherence is assumed to occur before interactions, breaking time-reversal symmetry.
• The paper establishes that the two forms are mutually incompatible and cannot be experimentally distinguished at present due to lack of macroscopic antimatter systems.
• Future high-energy experiments, such as those producing antiatoms or quark-gluon plasma, may provide the necessary conditions to test these theoretical predictions.