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Appendix C: Functional Derivatives

  1. Hans Christian Öttinger

Published Online: 27 JAN 2005

DOI: 10.1002/0471727903.app3

Beyond Equilibrium Thermodynamics

Beyond Equilibrium Thermodynamics

How to Cite

Öttinger, H. C. (2005) Appendix C: Functional Derivatives, in Beyond Equilibrium Thermodynamics, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471727903.app3

Publication History

  1. Published Online: 27 JAN 2005
  2. Published Print: 2 MAR 2005

ISBN Information

Print ISBN: 9780471666585

Online ISBN: 9780471727903



  • first and second functional derivatives;
  • extremization of functionals;
  • constraints


In the formulation of the GENERIC framework of beyond-equilibrium thermodynamics, functional derivatives of the energy and entropy play a central role. In this appendix, we first develop the basic formulas for calculating functional derivatives, we then present some conditions for the existence of extrema of functionals, and we finally describe how constraints on the independent variables can be incorporated into such calculations of functional derivatives. After the presentation of the basic definitions, all the developments are performed in terms of specific examples.