The adaptive coupling upper bound for the Wasserstein separation: microscopic flips against the macroscopic symmetry cost

Q: What does this research mean for the field?

An x-adaptive coupling establishes a new closed-form upper bound for the Connes-Rieffel distance W_1 between extreme broken-phase KMS states of a localized Bost-Connes system, improving upon the previously known trivial group-flip cost. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Ruqing Chen

doi:10.5281/zenodo.22429496

September 6, 2026Open Access

The adaptive coupling upper bound for the Wasserstein separation: microscopic flips against the macroscopic symmetry cost

View Full Paper

Ask AI

Bookmark

Share

Key Points

Establish a non-trivial upper bound for the Connes-Rieffel Wasserstein distance between extreme broken-phase KMS states in localized Bost-Connes systems.
Constructed an x-adaptive coupling method targeting states separated by a multiplicative order parameter.
Evaluated the competition between microscopic coordinate flips and macroscopic symmetry costs across state transitions.
Proved a closed-form upper bound on the Connes-Rieffel distance W_1 expressing the balance between microscopic flips and macroscopic symmetry costs.
Surpassed the previous benchmark limited strictly to the trivial group-flip cost w_0.

Ask about this paper

Answers are grounded in this paper and cite their sources.

Implication

Mathematical analysis demonstrates a refined Connes-Rieffel distance bound in broken-phase Bost-Connes systems, improving beyond standard group-flip costs.

Abstract

For the extreme broken-phase KMS states of a localized Bost-Connes system, separated by the order parameter chi(g) prod_j epsilon_j(x_j), the only known upper bound on the Connes-Rieffel distance W_1 was the trivial group-flip cost w_0. This paper constructs an x-adaptive coupling and proves the closed-form bound W_1 <= w_0 Pi_infinity + sum_k wj_k tauj_k prod_{l

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Ruqing Chen (2026) studied this question.

synapsesocial.com/papers/6a9fd77658e84d0ff5b46316 https://doi.org/10.5281/zenodo.22429496

View Full Paper

Ask AI

Bookmark

Share

The adaptive coupling upper bound for the Wasserstein separation: microscopic flips against the macroscopic symmetry cost

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

The adaptive coupling upper bound for the Wasserstein separation: microscopic flips against the macroscopic symmetry cost

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading