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Dynamical Conservation Laws in Quantum Spin Systems

  • Vojkan Jaksic
  • Claude-Alain Pillet
  • Anna Szczepanek
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Abstract

We study dynamical conservation laws and the propagation of thermodynamic structure in translation-invariant lattice quantum spin systems. Using Lieb-Robinson bounds [CMP 28 (1972), 251-257] in arbitrary dimension, and Araki's bounds [CMP 14 (1969), 120-157] in dimension one, we prove conservation of the specific entropy, specific energy, and specific relative entropy under suitable assumptions on the interactions. The transported local Hamiltonians admit surface energies that vanish per unit volume in the van Hove limit, and local observables remain a core for the transported generators at every finite time. Weak Gibbsianity is preserved for sufficiently small times in arbitrary dimension and for all times in dimension one. These results provide the analytical foundation for the structural theory of approach to equilibrium developed in a companion paper, and establish partial results toward the conjectures formulated there.

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Cite

BibTeXRIS
BibTeX
@misc{jaksic2026dynamical,
  title = {{Dynamical Conservation Laws in Quantum Spin Systems}},
  author = {Vojkan Jaksic and Claude-Alain Pillet and Anna Szczepanek},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21489},
  eprint = {2610.21489},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05801150v1},
  note = {CC BY-NC 4.0},
}
RIS
TY  - UNPB
TI  - Dynamical Conservation Laws in Quantum Spin Systems
AU  - Vojkan Jaksic
AU  - Claude-Alain Pillet
AU  - Anna Szczepanek
PY  - 2026
DA  - 2026/10/15
PB  - HAL
DO  - 10.48550/arxiv.2610.21489
UR  - https://hal.science/hal-05801150v1
AB  - We study dynamical conservation laws and the propagation of thermodynamic structure in translation-invariant lattice quantum spin systems. Using Lieb-Robinson bounds [CMP 28 (1972), 251-257] in arbitrary dimension, and Araki's bounds [CMP 14 (1969), 120-157] in dimension one, we prove conservation of the specific entropy, specific energy, and specific relative entropy under suitable assumptions on the interactions. The transported local Hamiltonians admit surface energies that vanish per unit volume in the van Hove limit, and local observables remain a core for the transported generators at every finite time. Weak Gibbsianity is preserved for sufficiently small times in arbitrary dimension and for all times in dimension one. These results provide the analytical foundation for the structural theory of approach to equilibrium developed in a companion paper, and establish partial results toward the conjectures formulated there.
ER  -