相关论文: Composability and Generalized Entropy

The concept of composability states that entropy of the total system composed of independent subsystems is a function of entropies of the subsystems. Here, the most general pseudoadditivity rule for composable entropy is derived based only…

We formulate, under general conditions, the problem of maximisation of the total entropy of the system, assumed to be in a composable form, for fixed total value of the constrained quantity. We derive the general form of the composability…

The requirement that an entropy function be composable is key: it means that the entropy of a compound system can be calculated in terms of the entropy of its independent components. We prove that, under mild regularity assumptions, the…

We show how the dependence of phase space volume $\Omega(N)$ of a classical system on its size $N$ uniquely determines its extensive entropy. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a…

We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one…

We consider the meta-equilibrium state of a composite system made up of independent subsystems satisfying the additive form of external constraints, as recently discussed by Abe [Phys. Rev. E {\bf 63}, 061105 (2001)]. We derive the additive…

An attempt is made to construct composable composite entropy with different $q$ indices of subsystems and address the H-theorem problem of the composite system. Though the H-theorem does not hold in general situations, it is shown that some…

Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers…

Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…

We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…

We review a new form of entropy suggested by us, with origin in mixing of states of systems due to interactions and deformations of phase cells. It is demonstrated that this nonextensive form also leads to asymmetric maximal entropy…

We construct the complete set of orders of growth and we define on it the generalized entropy of a dynamical systems. With this object we provide a framework where we can study the separation of orbits of a map beyond the scope of…

The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…

We analyze systematically composable composite entropy of two Tsallis subsystems with different q indices. H-theorem and thermal balance relation are commented.

The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general…

We present a general definition of entropy in the setting of pre-ordered semigroups, extending the notion of topological entropy. From our definition, we obtain the basic properties exhibited by various entropy-like theories encountered in…

Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…

Ordinary, macroscopic systems, naturally tend to a state of maximum entropy compatible with their constraints. However, this might not hold for gravity-dominated systems since their entropy may increase without bound unless this is…

This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…

In a quantum system, there may be many density matrices associated with a state on an algebra of observables. For each density matrix, one can compute its entropy. These are in general different. Therefore one reaches the remarkable…