Can Farther Beat Closer?

Quantum relaxation ordering in trapped-ion systems — an open research programme

Repository: github.com/quantum-relaxation-ordering
Stewards: Colla, Alessandra · Warring, Ulrich
Affiliation: Theory · Numerical · Experimental Quantum & Atomic Physics · Albert-Ludwigs-Universität Freiburg
Launched: 2026 · Version 0.1-alpha
Licence: CC BY 4.0 (text) · MIT (code)

Open Invitation

This repository is launched ahead of collaboration. It documents what is being done, how it is being done, and why—so that anyone who finds it interesting can see exactly where to step in. No promises, no predefined outcome. An opportunity to work together on something worth ordering properly.

What This Is

The Mpemba effect describes a situation in which a system initially farther from equilibrium relaxes faster than one closer to it. In classical thermodynamics this observation is ancient and contested. In quantum systems, a rigorous spectral interpretation has emerged over the past decade — and with it, the possibility of a precise, falsifiable experimental test.

This repository hosts a growing research programme aimed at realising such a test in a trapped-ion platform. It proceeds in public, solo at launch, with an open toolbox. Theory, numerics, tutorials, and eventually experimental data — all in one place, openly inspectable, freely usable.

Site Sections

01 — DOSSIER

Research Dossier

Consolidated overview: classical → stochastic → quantum regimes. The living document of the programme.

02 — FRAMEWORK

Falsifiable Framework

Which claim, which distance measure, which crossing. What would confirm or kill it.

03 — TUTORIALS

Tutorials

Lindblad dynamics, Liouvillian spectra, the reduced steady state (RSS). Open to all readers.

04 — NUMERICS

Numerics Toolbox

Python/QuTiP simulation pipeline. Live, growing, openly inspectable. Results rendered here.

05 — REFERENCES

References

Annotated landscape of classical, stochastic, and quantum Mpemba literature.

Current Focus

The immediate experimental target is the non-Markovian quantum Mpemba effect as defined by Strachan et al. (PRL 134, 220403, 2025). This work predicts qualitatively new crossing behaviour tied to bath memory structure — and makes quantitative predictions about crossing times and threshold asymmetries that can be tested on a trapped-ion platform.

The primary observable is the trace distance between the spin reduced state and the reduced steady state (RSS):

D(ρ, σ) = ½ Tr|ρ - σ| A quantum Mpemba effect is observed when: D(ρ_A(0), ρ_ss) > D(ρ_B(0), ρ_ss) [A starts farther] but τ_A < τ_B [A equilibrates faster]

Pre-Registration Commitment

The analysis method will be pre-registered before any experimental data are examined. This discipline is the point, not an obstacle. Numerical work and simulation tooling proceed in parallel and are documented here as they develop.

Contributors & Stewards

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GitBook Links

Two precursor documents live in the Ions in Freiburg open-science harbour:

Signatures of Equilibration — A Design-Space Map (Invariant Framework, v0.4)
Can "Farther" Beat "Closer"? A Falsifiable Framework for Quantum Relaxation Ordering (Essay)

This repository is the operational complement to those documents — where the code runs and the data will live.