Collective heat capacity for quantum thermometry and quantum engine enhancements

The performances of quantum thermometry in thermal equilibrium together with the output power of certain class of quantum engines share a common characteristic: both are determined by the heat capacity of the probe or working medium. After noticing that the heat capacity of spin ensembles can be significantly modified by collective coupling with a thermal bath, we build on the above observation to investigate the respective impact of such collective effect on quantum thermometry and quantum engines. We find that the precision of the temperature estimation is largely increased at high temperatures, reaching even the Heisenberg scaling - inversely proportional to the number of spins. For Otto engines operating close to the Carnot efficiency, collective coupling always enhances the output power. Some tangible experimental platforms are suggested.