References

Annotated landscape — from classical Mpemba to the quantum non-Markovian case

This is not a comprehensive review of the Mpemba literature. It is a curated map of the papers directly relevant to this programme, annotated for their role in the current experimental design. For a broader field overview see the viewpoint by Warring (Physics 17, 105, 2024) and references therein.

• ST25
  Strachan, D. A. et al. Quantum Mpemba Effect in Non-Markovian Open Systems. Physical Review Letters 134, 220403 (2025). doi:10.1103/PhysRevLett.134.220403 The primary theoretical target of this programme. Predicts qualitatively new crossings in trace distance tied to bath memory structure. Provides quantitative scaling of crossing time t* with bath memory time τ_bath. The robustness of these predictions against realistic spectral densities is the open question this programme addresses.

• MA19
  Manzano, G. et al. Quantum Mpemba Effect: How Faster Cooling Can Be. Physical Review Letters 122, 060604 (2019). One of the first rigorous treatments. Liouvillian spectral framework. Defines the quantum Mpemba effect as suppression of the slowest Liouvillian eigenmode in the initial state.
• CA20
  Carollo, F. et al. Exponentially Accelerated Approach to Stationarity in Markovian Open Quantum Systems through the Mpemba Effect. Physical Review Letters 127, 060401 (2020). Exponential speedup in open systems. Connects the Mpemba manifold to the geometry of Liouvillian spectra. Important for understanding what "farther but faster" means quantitatively.
• NF19
  Nava, A. & Fabrizio, M. Lindblad Dissipative Dynamics in the Presence of Phase Coexistence. SciPost Physics 9, 042 (2020). Mpemba effect in systems with phase coexistence. Relevant for understanding the role of initial-state structure near phase boundaries.
• AR23
  Ares, F. et al. Entanglement Asymmetry as a Probe of Symmetry Breaking. Nature Communications 14, 2036 (2023). Different measure, different mechanism. Uses entanglement asymmetry — not operative in our programme. Cited to document the definition-proliferation issue; see Framework page.
• PH24
  Warring, U. Viewpoint: Mpemba Effect Observed in a Trapped-Ion Quantum Simulator. Physics 17, 105 (2024). physics.aps.org/articles/v17/105 Field overview and critical assessment of the definition-proliferation problem. Starting point for orientation in the current programme.

• GO25
  [Paper sent by Schätz, Feb 2026] Physical Review Letters 133, 010402 (2024). doi:10.1103/PhysRevLett.133.010402 Experimental observation. To be annotated after full reading.
• NC25
  Recent NatComm — spin-boson with TI, noise added differently. Nature Communications (2025). doi:10.1038/s41467-025-59296-y Alternative realisation. Bath broadening implemented differently from Schätz group approach. Relevant for platform comparison and bath engineering strategy.

• LR17
  Lu, Z. & Raz, O. Nonequilibrium Thermodynamics of the Markovian Mpemba Effect and Its Inverse. PNAS 114, 5158 (2017). The spectral theory of the classical Mpemba effect. Defines the Mpemba condition as c₂ = 0 and the strong Mpemba effect. Foundational reference for the geometric picture in the Dossier.
• KR19
  Klich, I., Raz, O. et al. Mpemba Index and Anomalous Relaxation. Physical Review X 9, 021060 (2019). Introduces the Mpemba index. Characterises which initial states are on the Mpemba manifold. Important for the Module 3 state-space scan.
• BJ19
  Baity-Jesi, M. et al. The Mpemba Effect in Spin Glasses Is a Long-Range Memory Effect. PNAS 116, 15350 (2019). Mpemba effect in glassy systems. Long-range memory as classical analogue of non-Markovian bath. Useful background for the bath-memory interpretation.

• SC18
  Schätz, T. et al. Simulating Open Quantum Systems with Trapped Ions. New Journal of Physics 20, 053 (2018). doi:10.1088/1367-2630/aac87d Freiburg platform: spin-boson simulation with trapped ions. Bath broadening via sympathetic cooling with mixed-species ions. Primary reference for bath engineering strategy in this programme.
• CL16
  Clos, G. et al. Time-Resolved Observation of Thermalization in an Isolated Quantum System. Physical Review Letters 117, 170401 (2016). The 2016 Freiburg dataset originates from work in this period. This reference documents the experimental context. The dataset itself is under embargo pending pre-registration. See Dossier and Framework pages.

• EV10
  Esposito, M. & Van den Broeck, C. Three Detailed Fluctuation Theorems. Physical Review Letters 104, 090601 (2010). Non-equilibrium thermodynamics framework. Background for free-energy-based Mpemba measures — not the primary measure here, but relevant for interpretation.
• RP14
  Roldán, E. & Parrondo, J. M. R. Entropy Production Locally Averaged Over a Small Time Window. Physical Review E 85, 031129 (2012). Stochastic thermodynamics. Useful for understanding dissipation in Mpemba trajectories.

• GB24a
  Warring, U. Signatures of Equilibration — A Design-Space Map. Ions in Freiburg GitBook, Invariant Framework v0.4 (2024). gitbook link Classical Mpemba design-space map, originally framed for aqueous experiments. Precursor to the quantum framework in this repository.
• GB24b
  Warring, U. Can "Farther" Beat "Closer"? A Falsifiable Framework for Quantum Relaxation Ordering. Ions in Freiburg GitBook, Essay (2024). gitbook link The conceptual precursor to the Framework page in this repository. The Falsifiable Framework page here is the operational successor.