Abstract: Department of Medicinal Chemistry, Virginia Commonwealth University, Richmond, VA 23298,USAE-mail: kier@gems.vcu.edu* Author to whom correspondence should be addressed.Received: 21 November 1999 / Accepted: 28 January 2000 / Published: 4 February 2000Abstract: The formation of complex systems is accompanied by the emergence of proper-ties that are non-existent in the components. But what of the properties and behaviour ofsuch components caught up in the formation of a system of a higher level of complexity? Inthis assay, we use a large variety of examples, from molecules to organisms and beyond, toshow that systems merging into a complex system of higher order experience constraintswith a partial loss of choice, options and independence. In other words, emergence in acomplex system often implies reduction in the number of probable states of its components,a phenomenon we term dissolvence. This is seen in atoms when they merge to form mole-cules, in biomolecules when they form macromolecules such as proteins, and in macromole-cules when they form aggregates such as molecular machines or membranes. At higherbiological levels, dissolvence occurs for example in components of cells (e.g. organelles),tissues (cells), organs (tissues), organisms (organs) and societies (individuals).Far from being a destruction, dissolvence is understood here as a creative process in whichinformation is generated to fuel the process of self-organisation of complex systems, allow-ing them to appear and evolve to higher states of organisation and emergence. Questions areraised about the relationship of dissolvence and adaptability; the interrelation with top-down

Abstract: A class of dynamical systems associated to rings of S-integers in rational function fields is described. General results about these systems give a rather complete description of the well-known dynamics in one-dimensional additive cellular automata with prime alphabet, including simple formulae for the topological entropy and the number of periodic configurations. For these systems the periodic points are uniformly distributed along some subsequence with respect to the maximal measure, and in particular are dense. Periodic points may be constructed arbitrarily close to a given configuration, and rationality of the dynamical zeta function is characterized. Throughout the emphasis is to place this particular family of cellular automata into the wider context of S-integer dynamical systems, and to show how the arithmetic of rational function fields determines their behaviour. Using a covering space the dynamics of additive cellular automata are related to a form of hyperbolicity in completions of rational function fields. This expresses the topological entropy of the automata directly in terms of volume growth in the covering space.

Abstract: I ns tiu e of S c al Sc e ces I vo Pilar, Marulice rg 19/1, Zagreb, CrE-mail: Mislav.Stjepan.Zebec@ipdi.hr and Kreso.Perackovic@ipdi.hrReceived: 11 February 2000 / Accepted: 14 July 2000 / Published: 28 July 2000Abstract: Certain statistical aspects of social systems are described by appropriately definedquantities named social potentials. Relations between social potentials are postulated bydrawing an analogy with thermodynamics relations between thermodynamic potentials, thusobtaining a toy model of some of the statistical properties of social systems. Within thismodel, an interpretation of a socially relevant acting (acting as opposed to action, see ref.[1]) that does not invoke structural changes in social systems, is given in terms of social po-tentials.Keywords: social systems theory, thermodynamics, social potentials, entropy and tempera-ture of social systems.IntroductionStudy of social systems requires the application of statistical methods to their description and givesresults of social system research in terms of statistical data. The existence of rich statistics usually, butnot necessarily, implies some underlying structure or even dynamics. Bearing in mind the very conceptof social systems, it is reasonable to assume the existence of some sort of dynamics describing socialsystems that leads to the observed statistics. The present level of knowledge of a quantitative descrip-tion of social systems [2] implies that the formulation of complete and consistent theory is a formidabletask.

Abstract: This paper examines the semiosic development of energy to information within a dyadic reality that operates within the contradictions of both classical and quantum physics. These two realities are examined within the three Peircean modal categories of Firstness, Secondness and Thirdness. The paper concludes that our world cannot operate within either of the two physical realities but instead filiates the two to permit a semiosis or information-generation of complex systems.

Abstract: Free energy and entropy are examined in detail from the standpoint of classical thermodynamics. The approach is logically based on the fact that thermodynamic work is mediated by thermal energy through the tendency for nonthermal energy to convert sponta-neously into thermal energy and for thermal energy to distribute spontaneously and uni-formly within the accessible space. The fact that free energy is a Second-Law, expendable energy that makes it possible for thermodynamic work to be done at finite rates is empha-sized. Entropy, as originally defined, is pointed out to be the capacity factor for thermal en-ergy that is hidden with respect to temperature; it serves to evaluate the practical quality of thermal energy and to account for changes in the amounts of latent thermal energies in sys-tems maintained at constant temperature. With entropy thus operationally defined, it is pos-sible to see that T ∆ S° of the Gibbs standard free energy relation ∆ G° = ∆ H° − T ∆ S° serves to account for differences or changes in nonthermal energies that do not contribute to ∆

Abstract: The International Symposium on Entropy was held at the Max-Planck-Institut fur Physik komplexer Systeme (Dresden, Germany, http://www.mpipks-dresden.mpg.de/) on June 25-28, 2000.[...]

Abstract: We interpret the Holographic Conjecture in terms of quantum bits (qubits). N-qubit states are associated with surfaces that are punctured in N points by spin networks' edges labelled by the spin-½ representation of SU(2), which are in a superposed quantum state of spin "up" and spin "down". The formalism is applied in particular to de Sitter horizons, and leads to a picture of the early inflationary universe in terms of quantum computation. A discrete micro-causality emerges, where the time parameter is being defined by the discrete increase of entropy. Then, the model is analysed in the framework of the theory of presheaves (varying sets on a causal set) and we get a quantum history. A (bosonic) Fock space of the whole history is considered. The Fock space wavefunction, which resembles a Bose-Einstein condensate, undergoes decoherence at the end of inflation. This fact seems to be responsible for the rather low entropy of our universe.

Abstract: We propose a new definition of entropy for any mass m, based on gravitation and through the concept of a gravitational cross section. It turns out to be proportional to mass, and therefore extensive, and to the age of the Universe. It is a Machian approach. It is also the number of gravity quanta the mass has emitted through its age. The entropy of the Uni-verse is so determined and the cosmological entropy problem solved.

Abstract: The entropy for a black hole in a de Sitter space is approached within the fram e- work of spacetime foam. A simple model made by N wormholes in a semiclassical ap- proximation, is taken under examination to compute the entropy for such a case. An exte n- sion to the extreme case when the black hole and cosmological horizons are equal is di s- cussed.

Abstract: By using the maximum entropy principle with Tsallis entropy we obtain a fragment size distribution function which undergoes a transition to scaling. This distribution function reduces to those obtained by other authors using Shannon entropy. The treatment is easily generalisable to any process of fractioning with suitable constraints.