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Zeitschrift für Physikalische Chemie

International journal of research in physical chemistry and chemical physics

Editor-in-Chief: Rademann, Klaus

IMPACT FACTOR 2018: 0.975
5-year IMPACT FACTOR: 1.021

CiteScore 2018: 1.20

SCImago Journal Rank (SJR) 2018: 0.327
Source Normalized Impact per Paper (SNIP) 2018: 0.391

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Volume 218, Issue 7


Lagrange and Hamilton Integrals and their Connection

Gerhard Dickel
Published Online: 2008-06-16 | DOI: https://doi.org/10.1524/zpch.218.7.867.35723


The object of the following is the change from Lagrange line integrals of single particles to Lagrange line integrals of systems of particles under the condition of the first law. The first problem is the historical variational principle as imagined by Bernoulli, whereas the second problem concerns the built up of thermodynamic systems from elementary integrals. Since thermodynamics disregards mechanisms governing the connection or the interaction of particles the built up of thermodynamic systems is possible if Lagrange integrals exhibiting addition theorems between the limits are taken into account.

Hilbert’s Independence Theorem involving the transition from the Lagrange to the Hamilton potential proved to be a suitable method to turn over from the mathematical Lagrange potentials to the Hamilton representation as used in physics. Caratheodory, basing his “Complete Figures of Calculus of Variation” on Hilberts conception has given the variational principle that minimizes the connection of the elementary Lagrange integrals being connected between the limits.

The extension of thermodynamics to integrals composed from components showing a connection between the limits yields important thermodynamic properties.

About the article

Published Online: 2008-06-16

Published in Print: 2004-07-01

Citation Information: Zeitschrift für Physikalische Chemie, Volume 218, Issue 7, Pages 867–880, ISSN (Online) 2196-7156, ISSN (Print) 0942-9352, DOI: https://doi.org/10.1524/zpch.218.7.867.35723.

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Gerhard Dickel
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