Second-order asymptotic expansion and thermodynamic interpretation of a fast-slow Hamiltonian system

Matthias Klar, Karsten Matthies, Johannes Zimmer

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This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey
includes, among others, classical techniques, such as the WKB approximation or the averaging method, as well as modern techniques, such as
the GENERIC formalism. The main part of this article combines ideas of some of these techniques and addresses the problem of deriving a reduced system for the slow degrees of freedom (DOF) of a fast-slow Hamiltonian
system. In the rst part, we derive an asymptotic expansion of the averaged evolution of the fast-slow system up to second-order, using weak
convergence techniques and two-scale convergence. In the second part, we determine quantities which can be interpreted as temperature and entropy of the system and expand these quantities up to second-order,
using results from the rst part. The results give new insights into the thermodynamic interpretation of the fast-slow system at dierent scales.
Original languageEnglish
Article number119
Number of pages32
JournalLetters in Mathematical Physics
Issue number6
Publication statusPublished - 23 Nov 2022


  • math-ph
  • math.CA
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  • math.MP


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