N ov 2 00 5 Dynamical entropy of generalized quantum Markov chains on gauge invariant C ∗ - algebras
نویسنده
چکیده
We prove that the mean entropy and the dynamical entropy are equal for generalized quantum Markov chains on gauge-invariant C∗-algebras.
منابع مشابه
Factors generated by C-finitely correlated states
We present several equivalent conditions for C-finitely correlated states defined on the UHF algebras to be factor states and consider the types of factors generated by them. Subfactors generated by generalized quantum Markov chains defined on the gauge-invariant parts of the UHF algebras are also discussed.
متن کاملN ov 2 00 2 DIMENSION AND DYNAMICAL ENTROPY FOR METRIZED C ∗ - ALGEBRAS
We introduce notions of dimension and dynamical entropy for unital Calgebras “metrized” by means of cLip-norms, which are complex-scalar versions of the Lip-norms constitutive of Rieffel’s compact quantum metric spaces. Our examples involve the UHF algebras Mp∞ and noncommutative tori. In particular we show that the entropy of a noncommutative toral automorphism with respect to the canonical cL...
متن کاملar X iv : m at h - ph / 0 41 10 55 v 1 1 6 N ov 2 00 4 Robustness of dynamical entropy
When quantifying the mixing properties of a quantum dynamical system in terms of dynamical entropy, the following scheme appears natural: observe the state of the system at regular time intervals while it evolves and determine the entropy produced over time. It is clear that this entropy will not only depend on the type of dynamics, but also on the type of observations. Intuitively, one can exp...
متن کاملN ov 2 00 5 Analyticity of Entropy Rate in Families of Hidden Markov Chains ∗
We prove that under a mild positivity assumption the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. We give examples to show how this can fail in some cases. And we study two natural special classes of hidden Markov chains in more detail: binary hidden Markov chains with an unambiguous symbol and binary Markov chains corrupted ...
متن کامل. ge n - ph ] 2 5 M ay 2 00 6 The CP ( N - 1 ) Affine Gauge Theory in the Dynamical Space - time
An attempt to build quantum theory of field (extended) objects without a priori space-time geometry has been represented. Space-time coordinates are replaced by the intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space CP (N − 1). The fate of quantum system mod-eled by the generalized coherent states is rooted in this manifold. Dynamical (state-dependent)...
متن کامل