A statistical mechanics of an oscillator associative memory with scattered natural frequencies

Analytic treatment of a non-equilibrium random system with large degrees of freedoms is one of most important problems of physics. However, little research has been done on this problem as far as we know. In this paper, we propose a new mean field theory that can treat a general class of a non-equilibrium random system. We apply the present theory to an analysis for an associative memory with oscillatory elements, which is a well-known typical random system with large degrees of freedoms.Comment: 8 pages, 4 figure

Statistical Entropy in General Equilibrium Theory

This essay seeks to develop an integrated account of the workings of statistical mechanics and thermodynamics as a theory of economic equilibrium. It begins with a probabilistic description of general systems (made out of numerous elements), based on the practice of statistical physics and the work of E. T. Jaynes, and a self-contained overview of the arguments that lead to the concept of statistical entropy as a measure of uncertainty or disorder and the maximum statistical entropy principle . This provides the conceptual setting for developing a statistical mechanical model of general equilibrium in pure exchange economies, inspired by the statistical theory of markets of Duncan K. Foley. Emphasis is placed in the derivation of the properties of the entropy function of an economy—the maximized statistical entropy as a function of the amounts of resources in that economy. We then show that the statistical equilibrium theory of pure exchange economies gives rise to a phenomenological or ‘macro’ theory of resource allocation in the image of classical thermodynamics (and the generalized thermodynamics of L. I. Rozonoer). We thus establish the fundamental principle of the phenomenological theory—the maximum entropy principle—and illustrate its use for the study of isolated and small open economies.statistical entropy, thermodynamics, general equilibrium, physics

Imperfect rationality, macroeconomic equilibrium and price rigidities

We introduce some elements of Prospect Theory into a general equilibrium model with monoolistic competition in the good market and real wage rigidities due to (right to manage or efficient) wage bargaining, or to efficiency wages. We show that, under these types of labor market frictions, an increase in workers’ loss aversion: (i) reduces the equilibrium wage and in this way increases potential output; (ii) induces workers to work and consume less and in this way decreases potential output. If the former effect is greater (smaller) than the latter one, loss aversion increases (decreases) potential output. We also show that, under all the types of labor market frictions we consider, if loss aversion reduces equilibrium output, it also enhances the plausibility of nominal price rigidities

Economics in Relation to Sociology: Dualisms and Vilfredo Pareto's Pluralistic Methodology

Many economists remember the masters of Lausanne for their important contributions to general equilibrium and welfare economics, but Leon Walras and Vilfredo Pareto both pursued much broader social research agendas. Walras did this within the general framework of economics, by complementing his ‘pure economics’ with ‘social economics’. Pareto, in contrast, first isolated economic theory from the influence of other social phenomena and distinguished between the result of theoretical economics and the concrete economic phenomenon. He then developed a general theory of social equilibrium which, inter alia, provided for a synthetic reconciliation of economics with sociology to understand the concrete phenomenon. This paper investigates the relationship between Pareto’s economics and his sociology. Its main contribution is the clarification of the pluralistic character of his methodology. This is done by considering how dualistic distinctions became an important device for Pareto, with particular reference to Sheila Dow’s notion of dualism and Andrew Mearman’s categories of dualism. Pareto’s pluralistic approach is shown as a neo-positive blend of ‘temporary’ Cartesian and non-Cartesian elements, which is not consistent with Dow’s own Babylonian approach to economics. The paper also reveals the economic phenomena that Pareto considered were dominated by sociological influences and, therefore, not amenable to Cartesian analysis.economic equilibrium, pluralism, Vilfredo Pareto, social equilibrium

Cournot–Nash equilibria in continuum games with non-ordered preferences.

In the usual framework of continuum games with externalities, we substantially generalize Cournot–Nash existence results [Balder, A unifying approach to existence of Nash equilibria, Int. J.Game Theory 24 (1995) 79–94; On the existence of Cournot–Nash equilibria in continuum games, J. Math. Econ. 32 (1999) 207–223; A unifying pair of Cournot–Nash equilibrium existence results, J. Econ. Theory 102 (2002) 437–470] to games with possibly non-ordered preferences, providing a continuum analogue of the seminal existence results by Mas-Colell [An equilibrium existence theorem without complete or transitive preferences, J. Math. Econ. 1 (1974) 237–246], Gale and Mas-Colell [An equilibrium existence theorem for a general model without ordered preferences, J. Math. Econ. 2 (1975) 9–15], Shafer and Sonnenschein [Equilibrium in abstract economies without ordered preferences, J. Math. Econ. 2 (1975) 345–348], Borglin and Keiding [Existence of equilibrium actions and of equilibrium: a note on the “new” existence theorems, J. Math. Econ. 3 (1976) 313–316] and Yannelis and Prabhakar [Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econ. 12 (1983) 233–245].Pure Cournot–Nash equilibrium; Continuum games; Non-ordered preferences; Feeble topology;

Competition, Consumer Welfare, and the Social Cost of Monopoly

Conventional deadweight loss measures of the social cost of monopoly ignore, among other things, the social cost of inducing competition and thus cannot accurately capture the loss in social welfare. In this Article, we suggest an alternative method of measuring the social cost of monopoly. Using elements of general equilibrium theory, we propose a social cost metric where the benchmark is the Pareto optimal state of the economy that uses the least amount of resources, consistent with consumers' utility levels in the monopolized state. If the primary goal of antitrust policy is the enhancement of consumer welfare, then the proper benchmark is Pareto optimality, not simply competitive markets. We discuss the implications of our approach for antitrust law as well as how our methodology can be used in practice for allegations of monopoly power given a history of price-demand observations.Monopoly power, Antitrust economics, Applied general equilibrium

Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the take-up/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of non-equilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e. for active motion, (b) interactions between the particles based on global couplings. We derive analytical expressions for the non-equilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref. updated. For related work see also: http://summa.physik.hu-berlin.de/~frank/active.htm

Distinguishing between the concepts of steady state and dynamic equilibrium in geomorphology

The development of the concept of equilibrium in geomorphology over the past 15 years has been marked by linguistic difficulties due, in part, to the interchangeable use of the terms, dynamic equilibrium and steady state. It is here proposed that the range of steady state conditions constitute a sub-set of the range of conditions of dynamic equilibrium. The application of General Systems Theory is responsible for the introduction to geomorphology of the term steady state which in the strictest sense refers to the tendency for constant forms to develop. Gilbert understood dynamic equilibrium to mean an adjustment between the processes of erosion and the resistance of the bedrock. More recently, Leopold and Langbein described dynamic or quasi-equilibrium as a state of energy distribution which does not necessarily involve any regularity of form. However, dynamic equilibrium finds expression over space and time, in the evolving regularity and mutual adjustment of form elements. The development of regular erosional landforms reflects the tendency of the energy conditions of a system to make the final adjustment to the most probable state. If the manner of landform evolution is the point in question, the concepts of dynamic equilibrium and steady state become clearly distinguishable and system boundaries must be precisely defined. In field studies the theoretical approach is often superseded by the pragmatic approach. However, unless the logical distinction between the two concepts is made in the first place confusion will continue to persist in geomorphic analysis

An Introduction to Breakdown Phenomena in Disordered Systems

The rupture of a medium under stress typifies breakdown phenomena. More generally, the latter encompass the dynamics of systems of many interacting elements governed by the interplay of a driving force with a pinning disorder, resulting in a macroscopic transition. A simple mean-field formalism incorporating these features is presented and applied to systems representative of fracture phenomena, social dilemmas, and magnets out of equilibrium. The similarities and differences in the corresponding mathematical structures are emphasized. The solutions are best obtained from a graphical method, from which very general conclusions may be drawn. In particular, the various classes of disorder distribution are treated without reference to a particular analytical or numerical form, and are found to lead to qualitatively different transitions. Finally, the notion of effective (or phenomenological) theory is introduced and illustrated for non-equilibrium disordered magnets.Comment: Pedagogical article published as part of a special issue on thermodynamics and statistical physics; 20 page