On the Uniqueness Theorem for Pseudo-Additive Entropies

The aim of this paper is to examine the role of thermodynamics, and in particular, entropy, for the development of economics within the last 150 years. The use of entropy has not only led to a significant increase in economic knowledge, but also to the emergence of such scientific disciplines as econophysics, complexity economics and quantum economics. Nowadays, an interesting phenomenon can be observed; namely, that rapid progress in economics is being made outside the mainstream. The first significant achievement was the emergence of entropy economics in the early 1970s, which introduced the second law of thermodynamics to considerations regarding production processes. In this way, not only was ecological economics born but also an entropy-based econometric approach developed. This paper shows that non-extensive cross-entropy econometrics is a valuable complement to traditional econometrics as it explains phenomena based on power-law probability distribution and enables econometric model estimation for non-ergodic ill-behaved (troublesome) inverse problems. Furthermore, the entropy economics has accelerated the emergence of modern econophysics and complexity economics. These new directions of research have led to many interesting discoveries that usually contradict the claims of conventional economics. Econophysics has questioned the efficient market hypothesis, while complexity economics has shown that markets and economies function best near the edge of chaos. Quantum economics has already appeared on the horizon, which recognizes money as a fundamental measurement device in the economy. The development of these sciences may indicate the need to reformulate all mainstream economics from its foundations.

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Section: Non-extensive Cross-entropy Econometricsmentioning

confidence: 99%

The Role of Entropy in the Development of Economics

Jakimowicz

2020

“…For example, it is then not possible to introduce a conditional entropy consistently [ 36 ] because the corresponding conditional entropy cannot be properly defined. This is related to the fact that the Kolmogorov definition of conditional probability is not generally valid for escort distributions [ 37 ]. Additional issues arise from the theory of statistical estimation, since only entropies of the form

, i.e., sum-form entropies, can fulfil the consistency axioms [ 38 ].…”

Section: Discussionmentioning

confidence: 99%

Information Geometric Duality of ϕ-Deformed Exponential Families

Korbel

Hanel

Thurner

2019

Self Cite

In the world of generalized entropies-which, for example, play a role in physical systems with sub-and super-exponential phasespace growth per degree of freedom-there are two ways for implementing constraints in the maximum entropy principle: linear-and escort constraints. Both appear naturally in different contexts. Linear constraints appear e.g. in physical systems, when additional information about the system is available through higher moments. Escort distributions appear naturally in the context of multifractals and information geometry. It was shown recently that there exists a fundamental duality that relates both approaches on the basis of the corresponding deformed logarithms (deformed-log duality). Here we show that there exists another duality that arises in the context of information geometry, relating the Fisher information of φ-deformed exponential families that correspond to linear constraints (as studied by J. Naudts), with those that are based on escort constraints (as studied by S.-I. Amari). We explicitly demonstrate this information geometric duality for the case of (c, d)-entropy that covers all situations that are compatible with the first three Shannon-Khinchin axioms, and that include Shannon, Tsallis, Anteneodo-Plastino entropy, and many more as special cases. Finally, we discuss the relation between the deformed-log duality and the information geometric duality, and mention that the escort distributions arising in the two dualities are generally different and only coincide for the case of the Tsallis deformation.

“…The most cited papers to Cluster #12 include [ 76 , 77 , 78 , 79 , 80 ], etc. Except a review about entropy application in the fields of mathematics and science [ 80 ], other papers mainly introduced the theoretical innovation or extension of different kinds of entropies, especially those that are related to entropy functionals [ 76 , 78 ]. It seems that Cluster #12 is sophisticated and has integrated with other entropy studies, so that research across different entropy areas and ensuing application may have potential for research.…”

Section: Reference Co-citation Networkmentioning

confidence: 99%

Twenty Years of Entropy Research: A Bibliometric Overview

Zhao

Wang

et al. 2019

Entropy, founded in 1999, is an emerging international journal in the field of entropy and information studies. In the year of 2018, the journal enjoyed its 20th anniversary, and therefore, it is quite reasonable and meaningful to conduct a retrospective as its birthday gift. In accordance with Entropy’s distinctive name and research area, this paper creatively provides a bibliometric analysis method to not only look back at the vicissitude of the entire entropy topic, but also witness the journal’s growth and influence during this process. Based on 123,063 records extracted from the Web of Science, the work in sequence analyzes publication outputs, high-cited literature, and reference co-citation networks, in the aspects of the topic and the journal, respectively. The results indicate that the topic now has become a tremendous research domain and is still roaring ahead with great potentiality, widely researched by different kinds of disciplines. The most significant hotspots so far are suggested as the theoretical or practical innovation of graph entropy, permutation entropy, and pseudo-additive entropy. Furthermore, with the rapid growth in recent years, Entropy has attracted many dominant authors of the topic and experiences a distinctive geographical publication distribution. More importantly, in the midst of the topic, the journal has made enormous contributions to major research areas, particularly being a spear head in the studies of multiscale entropy and permutation entropy.