Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00347064" target="_blank" >RIV/68407700:21340/21:00347064 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3390/e23010096" target="_blank" >https://doi.org/10.3390/e23010096</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/e23010096" target="_blank" >10.3390/e23010096</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

<a href="/cs/project/GA19-16066S" target="_blank" >GA19-16066S: Nelineární interakce a přenos informace v komplexních systémech s extrémními událostmi</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Entropy

ISSN

1099-4300

e-ISSN

1099-4300

Svazek periodika

23

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

10

Strana od-do

—

Kód UT WoS článku

000610106600001

EID výsledku v databázi Scopus

2-s2.0-85099283807