Second-order fast–slow dynamics of non-ergodic Hamiltonian systems: Thermodynamic interpretation and simulation

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

“…This simplified model has the advantage that the notation can be kept to a minimum while the most important results can still be conveyed to the reader. The results presented in this article do generalise to a system of multiple fast and slow particles [33,34]. The lowdimensional presentation we have chosen here, however, makes the arguments more transparent, and the extension to more complex situations is relatively straightforward.…”

“…This finding can potentially accelerate the simulation of slow dynamics in molecular dynamics simulations to higher accuracy. Some numerical experiments can be found in [33,34].…”

“…To study the dynamics of y ε and z ε for 0 < ε < ε 0 , a detailed asymptotic analysis is required. An in-depth description for the case of multiple fast and slow DOF can be found in [33], which similarly uses ideas from [5,39]. The proof sketches given below are conceptually similar to those in [33], but are more transparent due to less notational overhead.…”

“…An in-depth description for the case of multiple fast and slow DOF can be found in [33], which similarly uses ideas from [5,39]. The proof sketches given below are conceptually similar to those in [33], but are more transparent due to less notational overhead. The idea is to transform the fast DOF into action-angle variables.…”

“…The detailed proof of Theorem 1 was already carried out, in the case of multiple fast and slow DOF in [33]. For this reason, we will only summarise the essential steps and indicate the differences.…”