Operational and free-energy convergence do not determine kinetic geometry in logarithmic quantum transport
Abstract
For every primitive GNS-symmetric quantum Markov generator onMd(ℂ), d≥2, we construct reversible extensions on acountable direct sum with a common all-time diamond-norm semigroup limitand a common trace-norm Γ-limit of relative entropies. Theirentropy-constrained logarithmic current actions nevertheless have acontinuum of distinct Γ-limits. The additional cotangent form isχ(E−F0(B))|Q0Ceh|2, whereχ=limsupn bn/φn2 is determined by the auxiliary rates.The joint action--Fisher functional has instead the original core limit.For canonically embedded faithful initial data, the correspondingenergy--dissipation functionals Γ-converge, and their almostminimizers converge to the core semigroup. Every recovery family attaininga strict kinetic saving along a faithful C2 curve below the entropy caphas integrated Fisher cost bounded below by a positive multiple oflog2(1/δ). At fixed coupling, the current action need not belower semicontinuous and can strictly exceed the metric energy of itsinduced distance. A second construction has a faithful stationary limit,vanishing generator and all-time semigroup differences in diamond norm,and entropy Γ-convergence, but collapsing distances between fixedfaithful states. A bound in terms of the diamond norm of the entireauxiliary generator gives a complementary obstruction.
Related
- Geometry and Convergence of Quadratically Regularized Optimal Transport I
- Geometry and Convergence of Quadratically Regularized Optimal Transport II
- Deligne--Faltings Logarithmic Derived Geometry with a View towards Logarithmic GLSM
- Convergence of Singular Dynamics Driven by Mixed Logarithmic Heat Gradients
- Logarithmic transport at topological phase transitions of one-dimensional chiral quantum systems
BibTeX
@misc{anass2026operational,
title = {{Operational and free-energy convergence do not determine kinetic geometry in logarithmic quantum transport}},
author = {Nifa Anass},
howpublished = {HAL},
year = {2026},
month = jun,
doi = {10.5281/zenodo.22699067},
url = {https://hal.science/hal-05746506v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Operational and free-energy convergence do not determine kinetic geometry in logarithmic quantum transport
AU - Nifa Anass
PY - 2026
DA - 2026/06/10
PB - HAL
DO - 10.5281/zenodo.22699067
UR - https://hal.science/hal-05746506v1
AB - For every primitive GNS-symmetric quantum Markov generator onM_d(ℂ), d≥2, we construct reversible extensions on acountable direct sum with a common all-time diamond-norm semigroup limitand a common trace-norm Γ-limit of relative entropies. Theirentropy-constrained logarithmic current actions nevertheless have acontinuum of distinct Γ-limits. The additional cotangent form isχ(E−F_0(B))|Q_0Ce_h|^2, whereχ=limsup_n b_n/φ_n^2 is determined by the auxiliary rates.The joint action--Fisher functional has instead the original core limit.For canonically embedded faithful initial data, the correspondingenergy--dissipation functionals Γ-converge, and their almostminimizers converge to the core semigroup. Every recovery family attaininga strict kinetic saving along a faithful C^2 curve below the entropy caphas integrated Fisher cost bounded below by a positive multiple oflog^2(1/δ). At fixed coupling, the current action need not belower semicontinuous and can strictly exceed the metric energy of itsinduced distance. A second construction has a faithful stationary limit,vanishing generator and all-time semigroup differences in diamond norm,and entropy Γ-convergence, but collapsing distances between fixedfaithful states. A bound in terms of the diamond norm of the entireauxiliary generator gives a complementary obstruction.
ER -