A possible deformed algebra and calculus inspired in nonextensive thermostatistics

By Ernesto P. Borges. 2003

370 citations recorded by the source corpus.

We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an eigenfunction. The q-derivative and the q-integral have a dual nature, that is also presented.

Subfields: Economics and Econometrics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9f6579757acc5cc2f9a51d494fcbdd9e0bec03b6

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Citations in the corpus

Thermodynamics (2021, neutral): “Important numerical methods to obtain approximations of the partition function and expectation values include, in particular, various Quantum Monte Carlo (QMC) techniques [1, 2].”
On non-Gaussianity and dependence in financial time series: a nonextensive approach (2005, methodology): “…(Lévy 1948, 1954)) using either the general definition of convolution (S. Abe, private communication), convolution based on the generalized algebra by Borges (2004) or through generalized Green functions (R.S. Mendes, private communication), but, until now, without success, hence making this…”
Nonadditive entropy and nonextensive statistical mechanics - An overview after 20 years (2009, background): “It is sometimes introduced through the q-product [48, 49]”