Mass and free energy in the thermodynamics of squashed Kaluza-Klein black holes

The Abbott-Deser mass, the Hamiltonian and the Komar mass of the five-dimensional Kaluza-Klein black hole with squashed horizons take different values. Introducing a new couple of thermodynamic variables for the Komar mass, we show that each mass can be interpreted as a thermodynamic potential with its own natural variables, i.e. all masses are related to each other by the Legendre transformations. It is found that the new variables and the gravitational tension represent the squashing of the outer horizon.