Projection-Operator Method

  1. Hans Christian Öttinger

Published Online: 27 JAN 2005

DOI: 10.1002/0471727903.ch6

Beyond Equilibrium Thermodynamics

Beyond Equilibrium Thermodynamics

How to Cite

Öttinger, H. C. (2005) Projection-Operator Method, in Beyond Equilibrium Thermodynamics, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471727903.ch6

Publication History

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

ISBN Information

Print ISBN: 9780471666585

Online ISBN: 9780471727903



  • nonequilibrium statistical mechanics;
  • coarse-graining;
  • nonequilibrium ensembles;
  • projection-operator approach;
  • atomistic expressions for GENERIC building blocks;
  • Markovian time-evolution


This chapter deals with the foundations of nonequilibrium statistical mechanics or, in more descriptive words, with the theory of coarse-graining for classical dynamical systems. The goal is to obtain thermodynamic information about a nonequilibrium system from more detailed levels of description, in particular, from the atomistic level. Atomistic expressions for the GENERIC building blocks are derived, where the procedure is strongly inspired by equilibrium statistical mechanics and its role as a background for phenomenological thermodynamics. The derivation relies on the projection-operator approach, keeping sufficiently many variables and the appropriate nonlinearities to achieve a realistic description of a system by Markovian time-evolution equations.