Physica A 304 (2002) 525–534 www.elsevier.com/locate/physa Analysis of resources distribution in economics based on entropy I. Antoniou a; b; ∗ , V.V. Ivanov a; c , Yu.L. Korolev d , A.V. Kryanev a; d , V.V. Matokhin d , Z. Suchanecki a; e a International Solvay Institutes for Physics and Chemistry, Bd. du Triomphe, CP-231, Campus Plaine ULB, 1050 Brussels, Belgium b Theoretische Natuurkunde, Free University of Brussels, Brussels, Belgium c Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980, Dubna, Russia d Moscow Engineering and Physical Institute, 115409, Moscow, Russia e Institute of Mathematics, University of Opole, ul. Oleska 48, 45-052 Opole, Poland Received 28 June 2001 Abstract We propose a new approach to the problem of ecient resources distribution in dierent types of economic systems. We also propose to use entropy as an indicator of the eciency of resources distribution. Our approach is based on methods of statistical physics in which the states of economic systems are described in terms of the density functions  (g; ) of the variable g parametrized by . The parameter  plays a role of the integral characteristic of the state of the economic system. Having the density function  (g; ) we can use the corresponding entropy to evaluate the eciency of the resources distribution. Our theoretical study have been tested on real data related to the portfolio investment. c  2002 Elsevier Science B.V. All rights reserved. 1. Introduction A key issue in economics consists of the ecient distribution of resources [1]. Usually resource distribution problems are solved for economic systems consisting of a large number of components. Such macroeconomic systems has been recently studied using the well-developed and ecient methods of statistical physics [2–5]. In this approach the state of economic system is described by a probability distribution [6–8]. Using the density function one can calculate the corresponding entropy functional. Conservation of entropy in time may indicate the absence of macroscopic changes * Corresponding author. Tel.: +32-2-650-55-33; fax: +32-2-650-50-28. E-mail address: iantonio@vub.ac.be (I. Antoniou). 0378-4371/02/$-see front matter c  2002 Elsevier Science B.V. All rights reserved. PII:S0378-4371(01)00575-1