  One-dimensional systems, such as nanowires or electrons moving along strong
magnetic field lines, have peculiar thermalization physics. The binary
collision of point-like particles, typically the dominant process for reaching
thermal equilibrium in higher dimensional systems, cannot thermalize a 1D
system. We study how dilute classical 1D gases thermalize through three-body
collisions. We consider a system of identical classical point particles with
pairwise repulsive inverse power-law potential $V_{ij} \propto 1/|x_i-x_j|^n$
or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute
a collision kernel and use it in the Boltzmann equation to evolve a perturbed
thermal state with temperature $T$ toward equilibrium. We explain the shape of
the kernel and its dependence on the system parameters. Additionally, we
implement molecular dynamics simulations of a many-body gas and show agreement
with the Boltzmann evolution in the low density limit. For the inverse
power-law potential, the rate of thermalization is proportional to $\rho^2
T^{\frac{1}{2}-\frac{1}{n}}$ where $\rho$ is the number density. The
corresponding proportionality constant decreases with increasing $n$.
