  In one dimension, particles can not bypass each other. As a consequence, the
mean-squared displacement (MSD) in equilibrium shows sub-diffusion ${\rm
MSD}(t)\sim t^{1/2}$, instead of normal diffusion ${\rm MSD}(t)\sim t$. This
phenomenon is the so-called single-file diffusion. Here, we investigate how the
above equilibrium behaviors are modified far from equilibrium. In particular,
we want to uncover what kind of non-equilibrium driving force can suppress
diffusion and achieve the long-range crystalline order in one dimension, which
is prohibited by the Mermin-Wagner theorem in equilibrium. For that purpose, we
investigate the harmonic chain driven by the following four types of driving
forces that do not satisfy the detailed balance: (i) temporally correlated
noise with the noise spectrum $D(\omega)\sim \omega^{-2\theta}$, (ii)
conserving noise, (iii) periodic driving force, and (iv) periodic deformations
of particles. For the driving force (i) with $\theta>-1/4$, we observe ${\rm
MSD}(t)\sim t^{1/2+2\theta}$ for large $t$. On the other hand, for the driving
forces (i) with $\theta<-1/4$ and (ii)-(iv), MSD remains finite. As a
consequence, the harmonic chain exhibits the crystalline order even in one
dimension. Furthermore, the density fluctuations of the model are highly
suppressed in a large scale in the crystal phase. This phenomenon is known as
hyperuniformity. We discuss that hyperuniformity of the noise fluctuations
themselves is the relevant mechanism to stabilize the long-range crystalline
order in one dimension and yield hyperuniformity of the density fluctuations.
