O(N) Fluctuations and Lattice Distortions in 1-Dimensional Systems

Statistical mechanics harmonizes mechanical and thermodynamical quantities, via the notion of local thermodynamic equilibrium (LTE). In absence of external drivings, LTE becomes equilibrium tout court, and states are characterized by several thermodynamic quantities, each of which is associated with negligibly fluctuating microscopic properties. Under small driving and LTE, locally conserved quantities are transported as prescribed by linear hydrodynamic laws, in which the local material properties of the system are represented by the transport coefficients. In 1-dimensional systems, on the other hand, various anomalies are reported, such as the dependence of the heat conductivity on the global state, rather than on the local state. Such deductions, that rely on the existence of thermodynamic quantities like temperature and heat, are here interpreted within the framework of boundary driven 1-dimensional Lennard-Jones chains of N oscillators. It is found that these chains experience non-negligible O(N) lattice distortions, resulting in strongly inhomogeneous systems, and O(N) position fluctuations, that are in contrast with the requirements of LTE