# $O(N)$ fluctuations and lattice distortions in 1-dimensional systems

## TL;DR

This paper investigates how 1D Lennard-Jones chains exhibit large-scale fluctuations and lattice distortions that challenge traditional hydrodynamic descriptions and energy flow assumptions.

## Contribution

It provides a novel interpretation of boundary-driven 1D systems showing $O(N)$ fluctuations and distortions, highlighting limitations of standard hydrodynamics.

## Key findings

- Observation of $O(N)$ lattice distortions in 1D chains
- Standard hydrodynamics does not apply due to large fluctuations
- Proposed modifications to energy flow models

## Abstract

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.