Deformed exponentials and logarithms in generalized thermostatistics
By Jan Naudts. 2002
159 citations recorded by the source corpus.
Criteria are given that κ-deformed logarithmic and exponential functions should satisfy. With a pair of such functions one can associate another function, called the deduced logarithmic function. It is shown that generalized thermostatistics can be formulated in terms of κ-deformed exponential functions together with the associated deduced logarithmic functions.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics, Statistics and Probability
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Citations in the corpus
- TriMap: Large-scale Dimensionality Reduction Using Triplets (2019, methodology): “[Update] We shift the final weights by subtracting the minimum weight value calculated over all triplets and applying a tempered log transformation, where ω min = min ( i (cid:48) ,j (cid:48) ,k (cid:48) ) ∈T ˜ ω i (cid:48) j (cid:48) k (cid:48) , and is called the tempered logarithm (Naudts, 2002).”
- Robust Bi-Tempered Logistic Loss Based on Bregman Divergences (2019, background): “logt : R+ Ñ R with temperature parameter t ě 0 as in [16]: logt(x) := 1 1 – t (x – 1) .”
- Generalized entropies and the transformation group of superstatistics (2011, background): “For a large class of distribution functions the duality relation of the associated glogarithms includes the condition Λ(x) = −Λ(1/x) [31] given in [16].”
- A more globally accurate dimensionality reduction method using triplets (2018, unknown): “We propose the following generalized log t -transformation where, the log t function (Naudts, 2002) is defined as Note that log t is concave and non-decreasing and generalizes the log function which is recovered at t = 1 .”