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The cold dark matter (CDM) structure formation scenario faces challenges on (sub)galactic scales, central among them being the `cusp-core' problem. A known remedy, driving CDM out of galactic centres, invokes interactions with baryons, through fluctuations in the gravitational potential arising from feedback or orbiting clumps of gas or stars. Here we interpret core formation in a hydrodynamic simulation in terms of a theoretical formulation, which may be considered a generalisation of Chandrasekhar's theory of two body relaxation to the case when the density fluctuations do not arise from white noise; it presents a simple characterisation of the effects of complex hydrodynamics and `subgrid physics'. The power spectrum of gaseous fluctuations is found to follow a power law over a range of scales, appropriate for a fully turbulent compressible medium. The potential fluctuations leading to core formation are nearly normally distributed, which allows for the energy transfer leading to core formation to be described as a standard diffusion process, initially increasing the velocity dispersion of test particles as in Chandrasekhar's theory. We calculate the energy transfer from the fluctuating gas to the halo and find it consistent with theoretical expectations. We also examine how the initial kinetic energy input to halo particles is redistributed to form a core. The temporal mass decrease inside the forming core may be fit by an exponential form; a simple prescription based on our model associates the characteristic timescale with an energy relaxation time. We compare the resulting theoretical density distribution with that in the simulation.