In this talk I will focus on the gravitational thermodynamics of the
far future. Cosmological observations suggest that most matter will be 
diluted away by the cosmological expansion, with the rest collapsing 
into supermassive black holes.
The likely future state of our local universe is a supermassive black
hole slowly evaporating in an empty universe dominated by a positive 
cosmological constant.
We describe the non-equilibrium thermodynamics of this process in
detail, showing that entropy is produced by heat from the black
hole flowing across the very cold cosmological horizon.
In contrast, flat Minkowski space is shown to have divergent entropy
and does not allow a direct computation of entropy production.
The talk will be largely based on http://arxiv.org/abs/1201.1298, 
which was submitted to Physical Review Letters in early January.