  Rich quantum effects emerge when several quantum systems are
indistinguishable from the point of view of the bath they interact with. In
particular, delocalised excitations corresponding to coherent superposition of
excited states appear and change drastically the dynamics and steady state of
the systems. Such phenomena, which are central mechanisms of superradiance,
present interesting properties for thermodynamics and potentially other quantum
technologies. Indeed, a recent paper [Phys. Rev. A 99, 052105 (2019)] studies
these properties in a pair of indistinguishable two-level systems and points
out surprising effects of mitigation and amplification of the bath's action on
the energy and entropy of the pair. Here, we generalise the study to ensembles
of arbitrary number of spins of arbitrary size (i.e. dimension). We confirm
that the previously uncovered mitigation and amplification effects remain, but
also that they become more and more pronounced with growing number of spins and
growing spin size. Moreover, we find that the free energy variation and the
entropy production associated with the bath-driven dissipation are
systematically reduced, formalising the idea of mitigation of the bath's
action. Most remarkably, the combination of mitigation effects from two baths
at different temperatures can result in amplifying their action. This is
illustrated with cyclic thermal machines, and leads to large power
enhancements. The reduction of irreversibility is also an interesting aspect
since irreversibility is known to limit the performance of thermodynamic tasks.
The above findings might also lead to interesting applications in collective
work extraction, quantum battery charging, state protection, light harvesting
devices, quantum biology, but also for the study of entropy production.
Moreover, some experimental realisations and observations suggest that such
effects are within reach.
