Thermodynamics and Mixtures on Configuration Space

  • Michael J. W. HallEmail author
  • Marcel Reginatto
Part of the Fundamental Theories of Physics book series (FTPH, volume 184)


We introduce the concept of a mixture of configuration space ensembles. In very general terms, if a physical system is described by the configuration space ensemble \((P_j,S_j)\) with probability \(w_j\), then it may be said to correspond to the mixture \(\{(P_j,S_j);w_j\}\). Mixtures for classical and quantum systems are shown to be equivalent to phase space densities and density operators, respectively, and obey corresponding classical and quantum Liouville equations. We also generalise d’Espagnat’s distinction between ‘proper’ and ‘improper’ quantum mixtures to mixtures of arbitrary configuration ensembles. With the help of mixtures it becomes possible to unify and generalise traditional classical and quantum approaches to thermodynamics, via the definition of suitable ‘thermal mixtures’ based on two universal primary notions: stationarity and distinguishability. Our formulation is very different to standard approaches based on the maximum entropy principle, and is equivalent to the standard statistical mechanics formulation in each of the quantum and classical cases. The latter case is of particular interest, as it provides a novel Hamilton–Jacobi picture of classical thermodynamics.


Phase Space Density Operator Configuration Space Jacobi Equation Stationary Ensemble 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Centre for Quantum DynamicsGriffith UniversityBrisbaneAustralia
  2. 2.Physikalisch-Technische BundesanstaltBraunschweigGermany

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