  The goal of this paper is to explore the potential multistability of the
climate of a planet around the habitable zone. A thorough investigation of the
thermodynamics of the climate system is performed for very diverse conditions
of energy input and infrared atmosphere opacity. Using PlaSim, an Earth-like
general circulation model, the solar constant S* is modulated between 1160 and
1510 Wm-2 and the CO2 concentration, [CO2], from 90 to 2880 ppm. It is observed
that in such a parameter range the climate is bistable, i.e. there are two
coexisting attractors, one characterised by warm, moist climates (W) and one by
completely frozen sea surface (Snowball Earth, SB). Linear relationships are
found for the two transition lines (W\rightarrowSB and SB\rightarrowW) in
(S*,[CO2]) between S* and the logarithm of [CO2]. The dynamical and
thermodynamical properties - energy fluxes, Lorenz energy cycle, Carnot
efficiency, material entropy production - of the W and SB states are very
different: W states are dominated by the hydrological cycle and latent heat is
prominent in the material entropy production; the SB states are predominantly
dry climates where heat transport is realized through sensible heat fluxes and
entropy mostly generated by dissipation of kinetic energy. We also show that
the Carnot efficiency regularly increases towards each transition between W and
SB, with a large decrease in each transition. Finally, we propose well-defined
empirical functions allowing for expressing the global non-equilibrium
thermodynamical properties of the system in terms of either the mean surface
temperature or the mean planetary emission temperature. This paves the way for
the possibility of proposing efficient parametrisations of complex
non-equilibrium properties and of practically deducing fundamental properties
of a planetary system from a relatively simple observable.
