Nonextensivity and Tsallis statistics in magnetic systems

Sampaio, Luiz C.; Albuquerque, Márcio P. de; Menezes, Fortunato Silva de

doi:10.1103/physrevb.55.5611

Cited by 45 publications

(40 citation statements)

References 19 publications

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“…The case of long-range interactions is more subtle. This case is conveniently discussed by introducing a variable such as the following one [34,35,36,37,38,39,40,41,42,43,44]:…”

Section: Generalizing Thermodynamicsmentioning

confidence: 99%

Inter-occurrence times and universal laws in finance, earthquakes and genomes

Tsallis

2016

Chaos, Solitons & Fractals

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A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy S BG and its associated exponential BG factor. Frequent behaviors in such complex systems have been shown to be closely related to q-statistics instead, based on the nonadditive entropy S q (with S 1 = S BG ), and its associated q-exponential factor which generalizes the usual BG one. In fact, a wide range of phenomena of quite different nature exist which can be described and, in the simplest cases, understood through analytic (and explicit) functions and probability distributions which exhibit some universal features. Universality classes are concomitantly observed which can be characterized through indices such as q. We will exhibit here some such cases, namely concerning the distribution of inter-occurrence (or interevent) times in the areas of finance, earthquakes and genomes.

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“…The case of long-range interactions is more subtle. This case is conveniently discussed by introducing a variable such as the following one [34,35,36,37,38,39,40,41,42,43,44]:…”

Section: Generalizing Thermodynamicsmentioning

confidence: 99%

Inter-occurrence times and universal laws in finance, earthquakes and genomes

Tsallis

2016

Chaos, Solitons & Fractals

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“…A first result was to obtain the scaling laws that follow from the application of Boltzmann-Gibbs statistics to a genuinely non-extensive system such as the LRIM in the regime α < d. The results for the internal energy, U, the magnetization M (defined as M = | N i=1 s i | and computed using Eq. (23)), the Helmholtz free energy F and the entropy S can be summarized by the following relations [26,27,18,[28][29][30]:…”

Section: The Scaling Functionsmentioning

confidence: 99%

Thermostatistics of extensive and non-extensive systems using generalized entropies

Salazar¹,

Toral²

2001

Physica A: Statistical Mechanics and its Applications

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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-range 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 case 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.

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“…4 ͑3͒ suggested by Tsallis 28 and later observed in Monte Carlo simulations. 26 Although field scaling gives rise to a significantly improved data collapse for m A / m B vs H and m A / m C vs H ͓Fig. 4͑a͒-4͑e͔͒, there is no significant improvement when considering m B / m C vs H ͓Fig.…”

Section: Instead Of Using the Resultsmentioning

confidence: 99%

“…From Eq. ͑1͒, it can be concluded that renormalization of U / N allows one to recover convergence according to U / ͑N ln N͒ → const for N → ϱ. Tsallis extended this reasoning to the Gibbs free energy, G. For a 3D system with dipolar interactions, Tsallis's scaling approach reads 26,28 …”

Section: Sample Preparationmentioning

confidence: 99%

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Nonextensivity in magnetic nanoparticle ensembles

Binek

Polisetty

et al. 2006

Phys. Rev. B

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A superconducting quantum interference device and Faraday rotation technique are used to study dipolar interacting nanoparticles embedded in a polystyrene matrix. Magnetization isotherms are measured for three cylindrically shaped samples of constant diameter but various heights. Detailed analysis of the isotherms supports Tsallis' conjecture of a magnetic equation of state that involves temperature and magnetic field variables scaled by the logarithm of the number of magnetic nanoparticles. This unusual scaling of thermodynamic variables, which are conventionally considered to be intensive, originates from the nonextensivity of the Gibbs free energy in three-dimensional dipolar interacting particle ensembles. Our experimental evidence for nonextensivity is based on the data collapse of various isotherms that require scaling of the field variable in accordance with Tsallis' equation of state.

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Nonextensivity and Tsallis statistics in magnetic systems

Cited by 45 publications

References 19 publications

Inter-occurrence times and universal laws in finance, earthquakes and genomes

Inter-occurrence times and universal laws in finance, earthquakes and genomes

Thermostatistics of extensive and non-extensive systems using generalized entropies

Nonextensivity in magnetic nanoparticle ensembles

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