Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

Korbel, Jan (2021) Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle. Entropy, 23 (1). p. 96. ISSN 1099-4300

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Abstract

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

Item Type: Article
Uncontrolled Keywords: maximum entropy principle; MaxEnt distribution; calibration invariance; Lagrange multipliers
Subjects: STM Repository > Physics and Astronomy
Depositing User: Managing Editor
Date Deposited: 13 May 2023 05:16
Last Modified: 24 May 2024 05:36
URI: http://classical.goforpromo.com/id/eprint/456

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