Research

Stochastic thermodynamics and active matter

Snapshot of a system of active particles exhibiting motility-induced phase separation: Particles cluster in some regions of the accessible volume, while other regions maintain a dilute, gas-like appearance, even though particle interactions are purely repulsive.

Complex systems at mesoscopic scales

• nano- to micrometer-sized systems
• examples: macromolecules, proteins, suspended colloids, bacteria
• no quantum effects, but strong thermal fluctuations
• stochastic dynamical systems (described by Langevin/Fokker-Planck equations)
• active matter: particles can consume energy from their environment to propel themselves forward persistently

Key results

• analyzing heat engines and their efficiency at mesoscopic scales
• fluctuation theorem for and thermodynamic interpretation of irreversibility in active matter systems

Math and physics of and with machine-learning models

Sketch of the three learning regimes and accuracy-efficiency tradeoff of RBMs. The regimes are characterized by the models divergence Δ_θ from the target distribution ("accuracy", the smaller the better) and its integrated autocorrelation time τ_θ ("efficiency", the smaller the better).

Machine-learning models as complex systems

• large number of elementary units
• relatively simple "microscopic laws" for their interactions
• complex "macroscopic" behavior emerging from the interplay of the elementary units

Key results

• largely universal learning characteristics of Restricted Boltzmann Machines (RBMs)
• hallucination-free reinforcement-learning framework for solving equations in symbolic form

Team

PhD students

• Konstantinos Georgakopoulos2024 ‐
• Siran Li2024 ‐

Publications

Peer-reviewed research articles

1. LD, C. Eidecker-Dunkel, and P. Reimann,
   Basis dependence of eigenstate thermalization,
   Phys. Rev. B 113, 094311 (2026)
2. LD,
   Temperature and conditions for thermalization after canonical quenches,
   Phys. Rev. B 112, 184307 (2025)
3. LD and R. Eichhorn,
   Thermodynamic nature of irreversibility in active matter,
   Phys. Rev. Research 7, 033077 (2025)
4. LD and P. Reimann,
   Random matrix approach to time-dependent forcing in many-body quantum systems,
   Phys. Rev. B 110, 144308 (2024)
5. LD and M. Ueda,
   Symbolic equation solving via reinforcement learning,
   Neurocomputing 613, 128732 (2024)
6. LD and P. Reimann,
   Stalled response near thermal equilibrium in periodically driven systems,
   Nat. Commun. 15, 294 (2024)
7. LD and M. Ueda,
   Three learning stages and accuracy-efficiency tradeoff of Restricted Boltzmann Machines,
   Nat. Commun. 13, 5474 (2022)
8. LD, P. Vorndamme, and P. Reimann,
   Thermalization of locally perturbed many-body quantum systems,
   Phys. Rev. B 105, 024310 (2022)
9. P. Reimann and LD,
   Refining Deutsch's approach to thermalization,
   Phys. Rev. E 103, 022119 (2021)
10. LD and P. Reimann,
    Typical relaxation of perturbed quantum many-body systems,
    J. Stat. Mech. 2021, 013106 (2021)
11. LD, S. Bo, and R. Eichhorn,
    How irreversible are steady-state trajectories of a trapped active particle?,
    J. Stat. Mech. 2021, 033216 (2021)
12. LD and R. Eichhorn,
    Irreversibility in active matter: General framework for active Ornstein-Uhlenbeck particles,
    Front. Phys. 8, 582992 (2021)
13. LD, P. Vorndamme, and P. Reimann,
    Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure,
    Phys. Rev. Research 2, 033210 (2020)
14. LD and P. Reimann,
    Persistent many-body quantum echoes,
    Phys. Rev. Research 2, 023216 (2020)
15. LD and P. Reimann,
    Predicting imperfect echo dynamics in many-body quantum systems,
    Z. Naturforsch. A 75, 403 (2020)
16. LD and P. Reimann,
    Relaxation theory for perturbed many-body quantum systems versus numerics and experiment,
    Phys. Rev. Lett. 124, 120602 (2020)
17. LD, H. Gies, and B. Knorr,
    Momentum dependence of quantum critical Dirac systems,
    Phys. Rev. D 99, 125019 (2019)
18. LD, S. Bo, and R. Eichhorn,
    Irreversibility in active matter systems: fluctuation theorem and mutual information,
    Phys. Rev. X 9, 021009 (2019)
19. S. Manikandan, LD, R. Eichhorn, and S. Krishnamurthy,
    Efficiency fluctuations in microscopic machines,
    Phys. Rev. Lett. 122, 140601 (2019)
20. P. Reimann and LD,
    Typicality of prethermalization,
    Phys. Rev. Lett. 122, 080603 (2019)
21. A. Argun, J. Soni, LD, S. Bo, G. Pesce, R. Eichhorn, and G. Volpe,
    Experimental realization of a minimal microscopic heat engine,
    Phys. Rev. E 96, 052106 (2017)

Dissertation

• LD,
  Predicting quantum many-body dynamics out of equilibrium,
  PhD Thesis, Bielefeld University (2021)

Teaching