Tsallis entropy and Jaynes' Information Theory formalism

Plastino, A.

doi:10.1590/s0103-97331999000100005

Cited by 111 publications

(67 citation statements)

References 1 publication

(2 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Many other authors use MaxEnt in conjunction with different entropic forms for which one of the four Khinchin's axioms is modified (the axiom of extensivity) [38,39], but keeping the original variables, not changing them as we do.…”

Section: Beyond Proportional Growth Generalizing Equation (35)mentioning

confidence: 99%

The workings of the maximum entropy principle in collective human behaviour

Hernando

Hernando²,

Plastino

et al. 2013

J. R. Soc. Interface.

Self Cite

View full text Add to dashboard Cite

We present an exhaustive study of the rank-distribution of city-population and population-dynamics of the 50 Spanish provinces (more than 8000 municipalities) in a time-window of 15 years (1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010). We exhibit compelling evidence regarding how well the MaxEnt principle describes the equilibrium distributions. We show that the microscopic dynamics that governs population growth is the deciding factor that originates the observed macroscopic distributions. The connection between microscopic dynamics and macroscopic distributions is unravelled via MaxEnt.

show abstract

Section: Beyond Proportional Growth Generalizing Equation (35)mentioning

confidence: 99%

The workings of the maximum entropy principle in collective human behaviour

Hernando

Hernando²,

Plastino

et al. 2013

J. R. Soc. Interface.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this paper, our discussion requires only the Jaynes Maximum entropy principle [13,14,15]. Jaynes' information theoretical approach to statistical mechanics based on the Shannon's extensive measure with a linear weighting of quantities as a mean value have successfully extended to Fisher's information measure( [6] and references therein).…”

Section: Introductionmentioning

confidence: 99%

On the robust thermodynamical structures against arbitrary entropy form and energy mean value

Yamano

2000

Eur. Phys. J. B

View full text Add to dashboard Cite

Abstract. We discuss that the thermodynamical Legendre transform structure can be retained not only for the arbitrary entropic form but also for the arbitrary form of the energy constraints by following the discussion of Plastino and Plastino. The thermodynamic relation between the expectation values and the conjugate Lagrange multipliers are seen to be universal. Furthermore, Gibbs' fundamental equation is shown to be unaffected by the choice of the entropy and the definition of the mean values due to the robustness of the Legendre transform structure.PACS. 05.70.-a Thermodynamics -05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)

show abstract

“…During the last decades the scientific community paid considerable attention to the generalization of concepts such as information, entropy [1][2][3][4] and differentiation [5][6][7][8]. Entropy was introduced in thermodynamics by Clausius and Boltzmann and was later adopted by Shannon and Jaynes in information theory [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Generalized Information

Machado

2014

Entropy

122

View full text Add to dashboard Cite

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

show abstract

Tsallis entropy and Jaynes' Information Theory formalism

Abstract: The role of Tsallis' non-extensive Information Measure within an a l a J a ynes Information-Theorybased formulation of Statistical Mechanics is discussed in rather detailed fashion.

Cited by 111 publications

References 1 publication

The workings of the maximum entropy principle in collective human behaviour

The workings of the maximum entropy principle in collective human behaviour

On the robust thermodynamical structures against arbitrary entropy form and energy mean value

Fractional Order Generalized Information

Contact Info

Product

Resources

About