caa a22 4500 378886452 CHVBK 20180305123444.0 cr unu---uuuuu 161128e20040701xx s 000 0 eng 10.1524/zpch.218.7.867.35723 doi (NATIONALLICENCE)gruyter-10.1524/zpch.218.7.867.35723 Dickel Gerhard Lagrange and Hamilton Integrals and their Connection [Elektronische Daten] [Gerhard Dickel] 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. © 2004 Oldenbourg Wissenschaftsverlag GmbH Thermodynamics & statistical physics nationallicence Laboratory techniques, experiments nationallicence Physical chemistry nationallicence Zeitschrift für Physikalische Chemie/International journal of research in physical chemistry and chemical physics Oldenbourg Wissenschaftsverlag GmbH 218/7/2004(2004-07-01), 867-880 0942-9352 218:7/2004<867 2004 218 zpch https://doi.org/10.1524/zpch.218.7.867.35723 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1524/zpch.218.7.867.35723 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dickel Gerhard NATIONALLICENCE 773 0- Zeitschrift für Physikalische Chemie/International journal of research in physical chemistry and chemical physics Oldenbourg Wissenschaftsverlag GmbH 218/7/2004(2004-07-01), 867-880 0942-9352 218:7/2004<867 2004 218 zpch CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter