Fig. 4: Approaching the prethermal state and thermodynamics.

aThe late-time relaxation of the average meson length M to the prethermal plateau is well-described by the prediction \(\langle {{{{{{{\mathcal{O}}}}}}}}(t)\rangle={{{{{{{{\mathcal{O}}}}}}}}}_{{{{{{{\rm{PreTh}}}}}}}}+{{\Delta }}{{{{{{{\mathcal{O}}}}}}}}F(t{{{{{{{\rm{v}}}}}}}}d{\rho }^{2})\). The quantity vd is obtained from a fit to the data. b The normalized one-meson phase-space occupation relaxes to a prethermal ensemble (prethermal: red continuous line; thermal: green dashed line; numerics: blue shaded area). Finite-density corrections are captured by the hard-rods approximation and cause an additional peak in the energy distribution P(E) (bottom). The relative difference in the meson densities between the thermal and prethermal ensemble Δρ = (ρ_PreTh − ρ_Th)/ρ_Th are Δρ = 0.16 and \({{\Delta }}\rho={{{{{{{\mathcal{O}}}}}}}}(1{0}^{-3})\) for \({h}_{\parallel }^{f}=0.015\) (top) and \({h}_{\parallel }^{f}=0.001\) (bottom), respectively. Thermal and prethermal observables are computed with Eq. (3), real-time evolution is obtained within the Truncated Wigner Approximation.