Understanding heat transport in one-dimensional systems remains a major challenge in theoretical physics, both from the quantum as well as from the classical point of view. In fact, steady states of one-dimensional systems are commonly characterized by macroscopic inhomogeneities, and by long-range correlations, as well as large fluctuations that are typically absent in standard three-dimensional thermodynamic systems. These effects violate locality—material properties in the bulk may be strongly affected by the boundaries, leading to anomalous energy transport—and they make more problematic the interpretation of mechanical microscopic quantities in terms of thermodynamic observables. Here, we revisit the problem of heat conduction in chains of classical nonlinear oscillators, following a Lagrangian and a Eulerian approach. The Eulerian definition of the flux is composed of a convective and a conductive component. The former component tends to prevail at large temperatures where the system behavior is increasingly gaslike. Finally, we find that the convective component tends to be negative in the presence of a negative pressure.
|Number of pages
|Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
|Early online date
|25 Sept 2019
|Published - Sept 2019
L.R. has been partially supported by Ministero dell'Istruzione dell'Università e della Ricerca (MIUR) Grant “Dipartimenti di Eccellenza 2018–2022”, Project No. E11G 18 000 35 000 1. C.M.M. thanks the Department of Mathematical Sciences of Politecnico di Torino for its hospitality and acknowledges financial support from the Spanish Government Grant No. PGC2018-099944-B-I00 (MCIU/AEI/FEDER, UE). This work started and developed while C.M.M. was a long-term Visiting Professor of Politecnico di Torino.