On classical and quantal Kolmogorov entropies
نویسنده
چکیده
The construction of a quantal Kolmogorov entropy that tends to the classical Kolmogorov entropy in the limit h -t 0 is discussed. The approach is to use sets of functions rather than disjoint partitions and involves the use of pseudo-differential operators.
منابع مشابه
A Survey on the Classical Limit of Quantum Dynamical Entropies
We analyze the behavior of quantum dynamical entropies production from sequences of quantum approximants approaching their (chaotic) classical limit. The model of the quantized hyperbolic automorphisms of the 2-torus is examined in detail and a semi-classical analysis is performed on it using coherent states, fulfilling an appropriate dynamical localization property. Correspondence between quan...
متن کاملClassical Limit of Quantum Dynamical Entropies
Two non-commutative dynamical entropies are studied in connection with the classical limit. For systems with a strongly chaotic classical limit, the Kolmogorov-Sinai invariant is recovered on time scales that are logarithmic in the quantization parameter. The model of the quantized hyperbolic automorphisms of the 2-torus is examined in detail.
متن کاملQuantum Dynamical Entropies and Gács Algorithmic Entropy
Several quantum dynamical entropies have been proposed that extend the classical Kolmogorov–Sinai (dynamical) entropy. The same scenario appears in relation to the extension of algorithmic complexity theory to the quantum realm. A theorem of Brudno establishes that the complexity per unit time step along typical trajectories of a classical ergodic system equals the KS-entropy. In the following,...
متن کاملar X iv : 0 70 8 . 27 79 v 1 [ m at h - ph ] 2 1 A ug 2 00 7 A Survey on the Classical Limit of Quantum Dynamical Entropies ∗
We analyze the behavior of quantum dynamical entropies production from sequences of quantum approximants approaching their (chaotic) classical limit. The model of the quantized hyperbolic automorphisms of the 2–torus is examined in detail and a semi–classical analysis is performed on it using coherent states, fulfilling an appropriate dynamical localization property. Correspondence between quan...
متن کاملEntropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analog...
متن کامل