Eur. Phys. J. B (2017) 90: 235
https://doi.org/10.1140/epjb/e2017-80364-4

Regular Article

Thermal response of a Fermi–Pasta–Ulam chain with Andersen thermostats

¹ Department of Information and Computing Science, Universiteit Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands
² Department of Physics and Astronomy, University of Padova, Via Marzolo 8, 35131 Padova, Italy
³ INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy

^a e-mail: f.dambrosio@uu.nl

Received: 21 June 2017
Received in final form: 27 September 2017
Published online: 4 December 2017

Abstract

The linear response to temperature variations is well characterised for equilibrium systems but a similar theory is not available, for example, for inertial heat conducting systems, whose paradigm is the Fermi–Pasta–Ulam (FPU) model driven by two different boundary temperatures. For models of inertial systems out of equilibrium, including relaxing systems, we show that Andersen thermostats are a natural tool for studying the thermal response. We derive a fluctuation-response relation that allows to predict thermal expansion coefficients or the heat capacitance in nonequilibrium regimes. Simulations of the FPU chain of oscillators suggest that estimates of susceptibilities obtained with our relation are better than those obtained via a small perturbation.