Active matter is the class of nonequilibrium systems where every constituent extracts energy from its environment to produce an autonomous sustained dynamics. Recently, some active models have focused on the collective dynamics of repulsive particles with oscillating shape. It has been shown that shape oscillation promotes deformation waves, in line with experiments for dense biological tissues, yielding a rich family of dynamical patterns which are reminiscent of instabilities observed in reaction-diffusion systems. The internship will study the thermodynamics of defects in pulsating active matter. The project will use some recent methods of stochastic thermodynamics to derive and examine the fluctuating hydrodynamics that describes the collective dynamics of defects. Overall, this study will largely build on the crosstalk between numerical and analytical methods of modern nonequilibrium statistical mechanics. In particular, the project will combine particle-based models and hydrodynamic theories.