Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Entropy Principle Exploited by Lagrange Multipliers

Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_60-1



A proper thermodynamic theory of mixtures avoids the so-called paradox of diffusion, by which disturbances in concentration propagate at infinite speeds. A theory with equations of balance of momenta for the constituents does that. Constraints on the constitutive functions are implied by the entropy principle which is exploited by use of Lagrange multipliers.


The entropy principle provides restrictions on the form of the constitutive functions in thermodynamics. And Lagrange multipliers are a convenient tool for the exploitation of such restrictions. The method is illustrated here for a mixture of inviscid fluids – a paradigmatic case.

The basis for a systematic theory of mixtures was laid down by Truesdell (1957), and Müller has developed its thermodynamics in several papers (Müller, 1968, 1973; Müller and Villaggio, 1976), the latter in collaboration with Villaggio. Those were...

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© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.Technical University BerlinBerlinGermany

Section editors and affiliations

  • Elena Ivanova
    • 1
  1. 1.Department of Theoretical Mechanics, Institute of Applied Mathematics and MechanicsPeter the Great St. Petersburg Polytechnic UniversitySt. PetersburgRussia