Reply to the Comment by T. Dauxois, F. Bouchet, S. Ruffo on the paper by A. Rapisarda and A. Pluchino, Europhysics News, 36 (2005) 202

TL;DR

This paper defends the application of Tsallis nonextensive statistical mechanics to the Hamiltonian Mean Field model against recent criticisms, emphasizing numerical evidence and clarifying misunderstandings about metastability and anomalous dynamics.

Contribution

It provides a rebuttal to critiques of using nonextensive statistics for the HMF model, highlighting numerical results and clarifying theoretical points.

Findings

Numerical evidence supports nonextensive approach to HMF model.

Criticism based on Vlasov approach is addressed and clarified.

The paper emphasizes the importance of metastability in the model's dynamics.

Abstract

In the comment by T.Dauxois et al.,(cond-mat/0605445), the authors question our application of the nonextensive statistical mechanics proposed by Tsallis, to explain the anomalous dynamics of the Hamiltonian Mean Field (HMF) model. More specifically they claim that the explanation of the metastability found in the out-of-equilibrium dynamics is only a fitting procedure and is also in contrast with a previous application. This criticism mostly relies on recent studies based on the Vlasov approach, where the authors claim to explain the anomalous behaviour of the HMF model in terms of a standard formalism. In order to reply to this comment we want to stress a few numerical facts and conclude with some final considerations. A recent paper by P-H. Chavanis (cond-mat/0604234) is also important to clarify the question here debated.