  Aims. We aim to understand how Hepsilon is formed in the quiet Sun. In
particular, we consider the particular physical mechanism that sets its source
function and extinction, how it is formed in different solar structures, and
why it is sometimes observed in emission. Methods. We used a 3D radiative
magnetohydrodynamic (MHD) simulation that accounts for non-equilibrium hydrogen
ionization, run with the Bifrost code. To synthesize Hepsilon and Ca II H
spectra, we made use of the RH code, which was modified to take into account
the non-equilibrium hydrogen ionization. To determine the dominant terms in the
H${\epsilon}$ source function, we adopted a multi-level description of the
source function. Using synthetic spectra and simulation, we studied the
contribution function to the relative line absorption or emission and compared
it with atmospheric quantities at different locations. Results. Our multi-level
source function description suggests that the H${\epsilon}$ source function is
dominated by interlocking, with the dominant interlocking transition being
through the ground level, populating the upper level of H${\epsilon}$ via the
Lyman series. This makes the H${\epsilon}$ source function partly sensitive to
temperature. The H${\epsilon}$ extinction is set by Lyman-${\alpha}$. In some
cases, this temperature dependence gives rise to H${\epsilon}$ emission,
indicating heating. High-resolution observations reveal that H${\epsilon}$ is
not just a weak absorption line. Regions with H${\epsilon}$ in emission are
especially interesting to detect small-scale heating events in the lower solar
atmosphere, such as Ellerman bombs. Thus, H${\epsilon}$ can be an important new
diagnostic tool for studies of heating in the solar atmosphere, augmenting the
diagnostic potential of Ca II H when observed simultaneously
