Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0409601

Equilibrium states and their entropy densities in gauge-invariant C*-systems

N. Akiho·F. Hiai·D. Petz
View original source ↗Read source document ↗Export metadata ↓

Abstract

A gauge-invariant C*-system is obtained as the fixed point subalgebra of the infinite tensor product of full matrix algebras under the tensor product unitary action of a compact group. In the paper, thermodynamics is studied on such systems and the chemical potential theory developed by Araki, Haag, Kastler and Takesaki is used. As a generalization of quantum spin system, the equivalence of the KMS condition, the Gibbs condition and the variational principle is shown for translation-invariant states. The entropy density of extremal equilibrium states is also investigated in relation to macroscopic uniformity.

Explore related subjects

math.OA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

N. Akiho, F. Hiai, D. Petz. 2005-03-16. Equilibrium states and their entropy densities in gauge-invariant C*-systems. https://doi.org/10.1142/s0129055x05002352

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Pointwise convergence of noncommutative discrete spherical ergodic averages

In this paper, we establish spherical maximal inequalities associated with commuting trace-preserving automorphisms on von Neumann algebras, extending Magyar-Stein-Wainger's discrete spherical maximal inequalities to the noncommutative setting. On a noncommutative probability space, we further prove that, under a strong ergodicity assumption, the corresponding discrete spherical averages converge bilaterally almost uniformly to $τ(x)1$ for every $x\in L_p(\mathcal M)$, $\frac{d}{d-2}<p\leq\infty$, when $d\geq5$.

math.OA↗
arXiv2026

Values of Rokhlin Dimension for Integer Actions

For an action of the integers on a C*-algebra, we show that the only possible values for the Rokhlin dimension (with commuting towers) are $0,1,2$ and $+\infty$. We study these values for certain classes of C*-algebras, and show that there is an automorphism of the Jiang--Su algebra with the property that its Rokhlin dimension with and without commuting towers are distinct.

math.OA↗
arXiv2026

Algebras, Kernels and Correspondences

This is a nearly complete draft of our paper in which we attempt to do three things. First, we show that when formulated in the context of reproducing kernel correspondences over Rieffel's category, Normod-$M$, the Kolmogorov decomposition/representation theorem of Ball, Marx, and Vinnikov is functorial in $M$. Second, we investigate relations between our work and the work of Clouâtre and Hartz concerning multipliers of reproducing kernels. This investigation leads to interesting questions about the geometry of the matricial unit disc associated with a correspondence over $M$. And third, we describe how some of the recent work of Salomon, Shalit and Shamovich may be formulated in our setting. This leads to the notion of subvarieties, their quotients, and their relation with the structure of reproducing correspondences.

math.OA↗