  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, the
transport coefficients often appear to depend on the global state, rather than
on the local state of the system at hand. We interpret these facts within the
framework of boundary driven 1-dimensional Lennard-Jones chains of $N$
oscillators, observing that they experience non-negligible $O(N)$ lattice
distortions and fluctuations. This implies that standard hydrodynamics and
certain expressions of energy flow do not apply in these cases. One possible
modification of the energy flow is considered.

Statistical Mechanics