Let (A,α) be a C∗-dynamical system. We introduce the notion of pressure Pα(H) of the automorphism α at a self-adjoint operator H ∈ A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant ∗-subalgebra A of A such that for all pairs a, b ∈ A the C∗-algebra they generate is finite dimensional, and there is p = p(a, b) ∈ N such that [α(a), b]...

Let E, belonging to the spectrum of H, be a fixed energy level. We are interested in the states for which the expected value of the energy equals E; i.e., in the states ρ such that ρ(H) = E. The classical result says that the maximal value of the entropy for such states is attained for a so-called Gibbs state; that is, a state with the density matrix e βH tr eβH for some β ∈ R. In this note, we...

We present a new derivation of the Onsager-Joyce-Montgomery (OJM) equilibrium statistical theory for point vortices on the plane, using the Bogoliubov-Feynman inequality for the free energy, Gibbs entropy function and Landau’s approximation. This formulation links the heuristic OJM theory to the modern variational mean field theories. Landau’s approximation is the physical counterpart of a larg...

In this paper we introduce a lemma. This lemma states that for a unitary covariant channel Ψ and a channel M such that M(ρ0) is of rank one for some state ρ0 ∈ S(H) the additivity of the minimal output entropy of Ψ implies that of Ψ ◦M , and the multiplicativity of the maximal output p-norm of Ψ, that of Ψ ◦M . For the product channel of the depolarising channel and an arbitrary channel the add...

We investigate factor maps of higher-dimensional subshifts of finite type. In particular, we are interested in how the number of ergodic measures of maximal entropy behaves under such factor maps. We show that this number is preserved under almost invertible maps, but not in general under finite to one factor maps. One of our tools, which is of independent interest, is a higher-dimensional char...

In this paper, we show that a surface group action on Sl with a non-zero Euler number has a positive topological entropy. We also show that if a surface group action on Sl has a Euler number which attains the maximal absolute value in the inequality of Milnor-Wood, then the topological entropy of the action equals the exponential growth rate of the group.

train energy saving problem investigates how to control train's velocity such that the quantity of energy consumption is minimized and some system constraints are satis ed. on the assumption that the train's weights on different links are estimated by fuzzy variables when making the train scheduling strategy, we study the fuzzy train energy saving problem. first, we propose a fuzzy energy ...

For any 1 ≤ r <∞, we build on the disk and therefore on any manifold, a C-diffeomorphism with no measure of maximal entropy. Résumé. Pour tout 1 ≤ r < ∞, nous construisons, sur le disque et donc sur toute variété, un difféomorphisme de classe C sans mesure d’entropie maximale.

We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability measures maximizing entropy and prove a multiplicative lower bound for the number of periodic points. This is intended as a step towards the understanding of s...

We introduced the concept of C-space entropy recently in [1–3] as a measure of knowledge of C-space for sensor-based path planning and exploration for general robot-sensor systems. The robot plans the next sensing action to maximally reduce the expected C-space entropy, also called the maximal expected entropy reduction, or MER criterion. The expected C-space entropy computation, however, made ...