相关论文: Entropy in type I algebras

A study of noncommutative topological entropy of gauge invariant endomorphisms of Cuntz algebras began in our earlier work with Joachim Zacharias is continued and extended to endomorphisms which are not necessarily of permutation type. In…

The entropy of a thermally isolated system should not decrease after a quench or external driving. For a classical system following Hamiltonian dynamics, we show how this statement emerges for a large system in the sense that the extensive…

In this paper we calculate the metric and folding entropies for a family of non-invertible symbolic dynamical systems $(\Sigma_{m_-,m_+}, \sigma_\phi)$ which generalizes the standard bilateral Bernoulli shifts. The space $\Sigma_{m_-,m_+}$…

We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical…

Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups. These include Kolmogorov--Sinai entropy based on F\o lner sequences for amenable groups, entropy defined using a random ordering of…

The definition of entropy obtained for stationary black holes is extended in this paper to the case of non-stationary black holes. Entropy is defined as a macroscopical thermodynamical quantity which satisfies the first principle of…

In this article we prove two formulas for the topological entropy of an F-optical Hamiltonian flow induced by a C^{\infty} Hamiltonian, where F is a Lagrangian distribution. In these formulas, we calculate the topological entropy as the…

In a recent paper [PRE 62, 4665 (2000)] (quant-ph/0203102) Manfredi and Feix proposed an alternative definition of quantum entropy based on Wigner phase-space distribution functions and discussed its properties. They proposed also some…

We construct a complete set of Wannier functions which are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability…

The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is…

The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…

We obtain the entropy and the surface entropy of the axial products on $\mathbb{N}^d$ and the $d$-tree $T^d$ of two types of systems: the subshift and the multiplicative subshift.

The von Neumann entropy of a density matrix of dimension d, expressed in terms of the first d-1 integer order R\'enyi entropies, is monotonically increasing in R\'enyi entropies of even order and decreasing in those of odd order.

Suppose F is a finite set of selfadjoint elements in a tracial von Neumann algebra M. For $\alpha >0$, F is $\alpha$-bounded if the free packing $\alpha$-entropy of F is bounded from above. We say that M is strongly 1-bounded if M has a…

The entanglement entropy of a subsystem $A$ of a quantum system is expressed, in the replica method, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix $\tr\rho_A^n$. We study the…

A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in…

Consider a state of a system with several subsystems. The entropies of the reduced state on different subsystems obey certain inequalities, provided there is an equivalence relation, and a function measuring volumes or weights of…

The combinatorial basis of entropy by Boltzmann can be written $H= {N}^{-1} \ln \mathbb{W}$, where $H$ is the dimensionless entropy of a system, per unit entity, $N$ is the number of entities and $\mathbb{W}$ is the number of ways in which…

We study questions motivated by results in the classical theory of dynamical systems in the context of triangulated and A-infinity categories. First, entropy is defined for exact endofunctors and computed in a variety of examples. In…

In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting…