  AGN outflows are the heat given up when gas in a galaxy evolves towards
thermodynamic equilibrium. Indeed, while AGN feedback regulates the growth of
massive galaxies, its origins can be understood as the spontaneous
thermodynamic process which ensures that the (Gibbs) free energy of the system
always decreases, enabling the galaxy to reach a more energetically favourable
state. In particular, it is shown that feedback heating processes will be
favoured whenever the hot atmosphere of a galaxy would effectively gain energy
as a result of cooling. For example, as the hot atmosphere of a galaxy cools
and contracts, the work done by gravity will be thermalised, with a fraction of
the gas also being captured by stars and the supermassive black hole at the
centre of the galaxy. If this gain of energy exceeds the loss of energy that
occurs when cooling gas drops out of the atmosphere, the Gibbs free energy of
the system would increase overall. Since this is energetically unfavourable,
feedback heating is initiated which acts to reduce the net cooling rate of the
atmosphere, thereby preventing any build-up of energy. The Gibbs free energy
can also decrease in the absence of feedback heating, but only if the loss of
energy due to mass dropping out of the atmosphere exceeds the gains of energy
described above. Therefore, to ensure that the Gibbs free energy always
decreases, a galaxy will necessarily flip between these two states,
experiencing episodes of heating and cooling. Due to the close long-term
balance between heating and cooling, the gas in a galaxy will evolve
quasi-statically towards thermodynamic equilibrium, which has the observable
appearance of galaxy growth being regulated by AGN feedback. The same mechanism
also provides an explanation for why strong AGN feedback occurs more frequently
in cool-core galaxy clusters than in non cool-core clusters.
