Boltzmann-Gibbsova porazdelitev denarja : delo diplomskega seminarja

Mehle, Tjaša (author), Vidmar, Matija (mentor)

To delo obravnava uporabo metod fizike na statističnih modelih za porazdelitev denarja, kot primer pristopa ekonofizike. V zaprtem gospodarskem sistemu se denar ohranja. Po analogiji z energijo mora ravnotežje verjetnostne porazdelitve denarja slediti Boltzmann-Gibbsovem zakonu, pri čemer je efektivna temperatura enaka povprečnemu znesku denarja na agenta. Numerične simulacije kažejo, da to drži vsaj takrat, ko je število agentov in povprečni znesek denarja na agenta velik. Glavni cilj diplomskega dela je ta rezultat dokazati.

• Language: Slovenian
• Keywords: statistična mehanika, Boltzmann-Gibbsov zakon, gospodarstvo, verjetnostna porazdelitev, stacionarna porazdelitev, simetrija obrata časa, ohranitveni zakon, Markovske verige
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-118034
• UDC: 519.2
• COBISS.SI-ID: 33316611
• Publication date in RUL: 15.08.2020

Secondary language

• Language: English
• Title: The Boltzmann-Gibbs distribution of money

Abstract

This paper is concerned with the application of the methods of physics to statistical models for money distribution as an example of the approach of econophysics. In a closed economic system, money is conserved. By analogy with energy, the equilibrium probability distribution of money must follow the exponential Boltzmann-Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. Numerical simulations suggest that at least when the number of agents and the average amount of money per agent are large, this is true. The main objective of this paper is to give a rigorous proof of this result.

• Keywords: statistical mechanics, Boltzmann-Gibbs law, economy, probability distribution, stationary distribution, time-reversal symmetry, conservation law, Markov chains