Thermostatistics of extensive and non-extensive systems using generalized entropies

R. Salazar and R. Toral

Physica A: Statistical Mechanics and its Applications, 2001, vol. 290, issue 1, 159-191

Abstract: We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a large number of degrees of freedom, and both short- and long-range interactions. The first method is quite general and it is based on the numerical evaluation of the density of states with a given energy. The second method is more specific for Tsallis thermostatistics and it is based on a standard Monte Carlo Metropolis algorithm along with a numerical integration procedure. We show here that both methods are robust and efficient. We present results of the application of the methods to the one-dimensional Ising model both in a short-range and in a long-range (non-extensive) case. We show that the thermodynamic potentials for different values of the system size N and different values of the non-extensivity parameter q can be described by scaling relations which are an extension of the ones holding for the Boltzmann–Gibbs statistics (q=1). Finally, we discuss the differences in using standard or non-standard mean value definitions in the Tsallis thermostatistics formalism and present a microcanonical ensemble calculation approach of the averages.

Keywords: Numeric simulations; Tsallis statistics; Long-range interactions; Monte Carlo simulations; Histogram methods; Non-extensive systems; Ising model (search for similar items in EconPapers)
Date: 2001
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:290:y:2001:i:1:p:159-191

DOI: 10.1016/S0378-4371(00)00361-7

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