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Article

Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

by 1,2,3
1
Section for the Science of Complex Systems, Center for Medical Statistics, Informatics, and Intelligent Systems (CeMSIIS), Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria
2
Complexity Science Hub Vienna, Josefstädterstrasse 39, 1080 Vienna, Austria
3
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, 11519 Prague, Czech Republic
Entropy 2021, 23(1), 96; https://doi.org/10.3390/e23010096
Received: 11 December 2020 / Revised: 7 January 2021 / Accepted: 9 January 2021 / Published: 11 January 2021
(This article belongs to the Special Issue The Statistical Foundations of Entropy)
The maximum entropy principle consists of two steps: The first step is to find the distribution which maximizes entropy under given constraints. The second step is to calculate the corresponding thermodynamic quantities. The second part is determined by Lagrange multipliers’ relation to the measurable physical quantities as temperature or Helmholtz free energy/free entropy. We show that for a given MaxEnt distribution, the whole class of entropies and constraints leads to the same distribution but generally different thermodynamics. Two simple classes of transformations that preserve the MaxEnt distributions are studied: The first case is a transform of the entropy to an arbitrary increasing function of that entropy. The second case is the transform of the energetic constraint to a combination of the normalization and energetic constraints. We derive group transformations of the Lagrange multipliers corresponding to these transformations and determine their connections to thermodynamic quantities. For each case, we provide a simple example of this transformation. View Full-Text
Keywords: maximum entropy principle; MaxEnt distribution; calibration invariance; Lagrange multipliers maximum entropy principle; MaxEnt distribution; calibration invariance; Lagrange multipliers
MDPI and ACS Style

Korbel, J. Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle. Entropy 2021, 23, 96. https://doi.org/10.3390/e23010096

AMA Style

Korbel J. Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle. Entropy. 2021; 23(1):96. https://doi.org/10.3390/e23010096

Chicago/Turabian Style

Korbel, Jan. 2021. "Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle" Entropy 23, no. 1: 96. https://doi.org/10.3390/e23010096

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