A notion of pressure with respect to a self-adjoint element is introduced for automorphisms of exact C*-algebras and a number of properties are established, including a generalization of a theorem of N. Brown for entropy asserting that the pressure remains the same upon passing to the extension of an automorphism to the crossed product. A variational inequality bounding the pressure below by the CNT and Sauvageot-Thouvenot free energies is obtained in two stages via a local state approximation entropy, which is shown to be an extension of M. Choda's nuclear entropy. We prove the variational principle for certain asymptotically Abelian automorphisms and introduce the class of weakly AF C*-algebras in order to describe a special subclass of these automorphisms.
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机译:对于精确的 C italic> *代数的自同构性,引入了关于自伴随元素的压力概念,并建立了许多性质,包括对N的一个定理的推广。当自同构扩展到交叉产物时,压力保持不变。通过局部状态近似熵,分两个阶段获得了由CNT和Sauvageot-Thouvenot自由能限制压力的变分不等式,这被证明是Choda核熵的扩展。我们证明了某些渐近阿贝尔自同构的变分原理,并介绍了弱AF C italic> *-代数的类别,以描述这些自同构的特殊子类。
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