  Emergence of hydrodynamics in quantum many-body systems has recently garnered
growing interest. The recent experiment of ultracold atoms [J. F. Wienand {\it
et al.}, arXiv:2306.11457] studied emergent hydrodynamics in hard-core bosons
using a bipartite fluctuation, which quantifies how the particle number
fluctuates in a subsystem. In this Letter, we theoretically study the variance
of a bipartite fluctuation in one-dimensional noninteracting fermionic dynamics
starting from an alternating state, deriving the exact solution of the variance
and its asymptotic linear growth law for the long-time dynamics. To compare the
theoretical prediction with the experiment, we generalize our exact solution by
incorporating the incompleteness of the initial alternating state, deriving the
general linear growth law analytically. We find that it shows quantitative
agreement with the experimentally observed variance growth without any fitting
parameters.
