  We present an extensive thermodynamic analysis of a hysteresis experiment
performed on a simplified yet Earth-like climate model. We slowly vary the
solar constant by 20% around the present value and detect a substantial
bistability: for a large range of values the realization of snowball (SB) or of
warm (W) climate conditions depend on the history of the system. Using recent
results on the global climate thermodynamics, we show that that the two regimes
feature radically different properties. The efficiency of the climate machine
increases with decreasing solar constant in W climate conditions, whereas the
opposite takes place in the SB regime. Instead, entropy production is
increasing with the solar constant in both branches of climate conditions, and
its value is about 4 times as large in the W branch than in the corresponding C
state. Finally, the degree of irreversibility of the system is much higher in
the W conditions, with an explosive growth in the upper range of the considered
values of solar constants. Whereas in the SB regime a dominating role is played
by changes in the meridional albedo contrast, in the W climate regime changes
in the intensity of latent heat fluxes are crucial for determining the observed
properties. This substantiates the importance of addressing correctly the
variations of the hydrological cycle in a changing climate. An interpretation
of the transitions at the boundary of the bistable region based upon
macro-scale thermodynamic properties is also proposed. Our results support the
adoption of a new generation of diagnostic tools based on the 2nd law of
thermodynamics for auditing climate model and outline a set of
parameterizations to be used in conceptual and intermediate complexity models
or for the reconstruction of the past climate conditions.
