Entropy principle of extremality as a driving force in the discrete dynamics of complex and living systems

Justification for the necessity of a new principle and mathematical model for the dynamics of complex and living systems is presented. The meaning of discrete time and space are discussed. Some patterns calculated from the new discrete dynamics demonstrate the possibilities of the proposed approach.     

Complexity and directional entropy in two dimensions

We study the directional entropy of a dynamical system associated to a Z² configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some direction is periodic. In particular, we show that all nonexpansive directions in a Z² system with the same local assumptions have zero directional entropy.     

Complexity in close binary evolution

The complex nature of close binary evolution is briefly reviewed. Population synthesis calculations of zero‐age cataclysmic variable stars (ZACVs) are presented using a common envelope (CE) efficiency parameter, α_CE, that is a function of the core mass of the primary. Specifically, we investigate the possibility that α_CE is different for CE evolution involving red giant branch (RGB) primaries than for asymptotic giant branch (AGB) primaries. We calculate a sequence of model orbital period distributions in present‐day ZACVs for 11 different combinations of efficiency parameters (α_RGB, α_AGB). We find that if CE evolution is much less efficient for RGB primaries than for AGB primaries (α_RGB ～ 0.1 or less), the number of CVs that form below 2 h is significantly decreased compared with standard constant α_CE models. © 2008 Wiley Periodicals, Inc. Complexity, 2008.     

Time aberration in living organisms: stochastic effects

A mathematical model for the determination of the value of a time interval as sensed by a living organism is discussed. This model extends previous work to include the fact that sensing may be a Gaussian white noise function of age.     

The student distribution and the principle of maximum entropy

Summary The Student distribution is obtained by means of the principle of maximum entropy.     

Local variational principle concerning entropy of a sofic group action

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic groups admitting a generating measurable partition with finite entropy; and then David Kerr and Hanfeng Li developed an operator-algebraic approach to actions of countable sofic groups not only on a standard probability space but also on a compact metric space, and established the global variational principle concerning measure-theoretic and topological entropy in this sofic context. By localizing these two kinds of entropy, in this paper we prove a local version of the global variational principle for any finite open cover of the space, and show that these local measure-theoretic and topological entropies coincide with their classical counterparts when the acting group is an infinite amenable group.     

Chemical reactions and the principle of maximal rate of entropy production

The author shows that the so-called standard equation of Chemical Kinetics is compatible with the principle of maximal rate of entropy production, but incompatible with Thermodynamics. The principle, on the other hand, is free of this defect and may be used to establish an improved version of the standard equation.

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Zusammenfassung Der Verfasser zeigt, daß die sogenannte Standardgleichung der chemischen Reaktionstechnik dem Prinzip der maximalen Entropieproduktion nicht widerspricht, wohl aber der Thermodynamik. Das Prinzip dagegen ist von diesem Mangel frei und kann zur Herleitung einer verbesserten Standardgleichung verwendet werden.

     

非自治动力系统Bowen估计熵的变分原理

推广了经典动力系统的Bowen拓扑熵,给出了非自治动力系统的Bowen估计熵的定义,讨论了非自治动力系统的Bowen估计熵和局部估计熵的关系,推广了自治动力系统Bowen拓扑熵的Billingsley型定理,研究了非自治动力系统的Bowen α-估计熵的Billingsley型定理.此外,给出了非自治动力系统Bowen...     

A minimum entropy principle of high order schemes for gas dynamics equations

The entropy solutions of the compressible Euler equations satisfy a minimum principle for the specific entropy (Tadmor in Appl Numer Math 2:211–219, 1986). First order schemes such as Godunov-type and Lax-Friedrichs schemes and the second order kinetic schemes (Khobalatte and Perthame in Math Comput 62:119–131, 1994) also satisfy a discrete minimum entropy principle. In this paper, we show an extension of the positivity-preserving high order schemes for the compressible Euler equations in Zhang and Shu (J Comput Phys 229:8918–8934, 2010) and Zhang et?al. (J Scientific Comput, in press), to enforce the minimum entropy principle for high order finite volume and discontinuous Galerkin (DG) schemes.     

Information sources with different cost scales and the principle of conservation of entropy

Summary The aim of this paper is to provide a mathematically rigorous and sufficiently general treatment of the basic information-theoretic problems concerning sources with symbols of different costs and noiseless coding in a general sense. The main new concepts defined in this paper are the entropy rate (entropy per unit cost) of a source with respect to a stochastic cost scale and the encoding (in particular decodable encoding) of a source in a general sense. On the basis of these concepts, we prove some general theorems on the relation of entropy rates with respect to different cost scales and on the effect of encoding to the entropy rate. In particular, the principle of conservation of entropy and the noiseless coding theorem are proved under very general conditions.The main results of this research have been reported at the Second Congress of Bulgarian Mathematicians, Varna, August 1967, at the International Symposium on Information Theory, San Remo, September 1967 and at the Colloquium on Information Theory, Debrecen, September 1967.     

On the principle of maximum entropy and the risk analysis of disaster loss

Disasters that occur everywhere in the most disordered way indicate that disaster entropy has reached the maximum value. Under given constraint conditions, when disaster entropy is the maximum value, the disaster loss series should follow P-III distribution. The occurrence interval of disaster loss refers to the average time interval that disaster loss of certain degree happens in the future. We could, according to the field disaster data and using P-III distribution function, calculate the value of future disaster loss with certain recurrence interval. Explicit in concept and easy to use, such a method has significant meaning in practice.     

146号初等元胞自动机的演化语言的复杂性

Symbolic dynamics of cellular automata is introduced by coarse-graining the temporal evolution orbits. Evolution languages are defined. By using the theory of formal languages and automata, the complexity of evolution languages of the elementary cellular automaton of rule 146 is studied and it is proved that its width 1-evolution language is regular, but for every n ≥ 2 its width n-evolution language is not context-free but context-sensitive. Also, the same results hold for the equivalent （under conjugation） elementary cellular automaton of rule 182.