Chromosphere of the quiet sun I. Shock and current-sheet dynamics and heating

Context. The solar chromosphere is a dynamic and crucial interface between the solar interior and its interplanetary environment, regulating how energy is locally deposited into heat and transported into the upper atmospheric layers. Despite significant observational and theoretical progress, the dominant processes responsible for chromospheric heating remain debated, particularly under quiet-Sun (QS) conditions. Aims. We aim to disentangle and quantify the respective roles of shocks and current sheets (CSs) in QS chromospheric modelling. Methods. We use a convection-zone-to-corona simulation performed with the radiation-magnetohydrodynamics code Bifrost. In order to identify shocks and CS events across space and time, we develop and apply physics-based criteria, allowing us to describe their dynamics and evaluate their contributions to both dissipative (viscous and ohmic) and mechanical (including compressive work) heating. Results. Shocks are found to dominate the energy deposition in the lower chromosphere (1 ≲ z ≲ 1.5 Mm), accounting for up to 59% of the mechanical heating rate near z = 1.2 Mm. In contrast, CSs become the primary contributor in the upper chromosphere (1.5 ≲ z ≲ 2.5 Mm), as both plasma β and Mach number Ma drop. Overall, 66% of the mechanical chromospheric heating is powered by the combined action of shocks and CSs, with 13% emerging from regions where shocks and CSs overlap, underscoring the pivotal role of dynamic coupling in the chromosphere. Conclusions. These results support a multi-process view of chromospheric heating in the QS, dominated by shocks, CSs, and non-steep gradient dynamics. In addition to viscous and ohmic dissipation, compressive heating can play a major role locally in the model, particularly in chromospheric shock structures, where it non-reversibly offsets cooling from expansion and radiation, and therefore constitutes a key heating contribution to consider in the energy budget. This study further highlights the need for next-generation observations to resolve the intermittent and small-scale nature of chromospheric dynamics, in order to bring new constraints on the coupling between the different layers of the solar atmosphere.