  We thoroughly investigate the microscopic mechanisms of the thermal transport
in orthorhombic \textit{o}-CsCu$_5$S$_3$ by integrating the
first-principles-based self-consistent phonon calculations (SCP) with the
linearized Wigner transport equation (LWTE). Our methodology takes into account
contributions to phonon energy shifts and phonon scattering rates from both
three- and four-phonon processes. Additionally, it incorporates the
off-diagonal terms of heat flux operators to calculate the total thermal
conductivity. The predicted $\kappa_\mathrm{L}$ with an extremely weak
temperature dependence following $\sim T^{-0.33}$, in good agreement with
experimental values along with the parallel to the Bridgman growth direction.
Such nonstandard temperature dependence of $\kappa_\mathrm{L}$ can be traced
back to the dual particlelike-wavelike behavior exhibited by thermal phonons.
Specifically, the coexistence of the stochastic oscillation of Cs atoms and
metavalent bonding among interlayer Cu-S atoms limits the particle-like phonon
propagation and enhances the wave-like tunneling of phonons. Simultaneously,
the electrical transport properties are determined by employing a precise
momentum relaxation-time approximation (MRTA) within the framework of the
linearized Boltzmann transport equation (LBTE). By properly adjusting the
carrier concentration, excellent thermoelectric performance is achieved, with a
maximum thermoelectric conversion efficiency of 18.4$\%$ observed at 800 K in
\textit{p}-type \textit{o}-CsCu$_5$S$_3$.} Our work not only elucidates the
anomalous thermal transport behavior in the copper-based chalcogenide
\textit{o}-CsCu$_5$S$_3$ but also provides insights for manipulating its
thermal and electronic properties for potential thermoelectric applications.
