Is sustainability a thermodynamic concept?

When calculating the 'degree of sustainability', socio-economic parameters and 'natural capital' are not easily quantified, and the question of the physical meaning of 'sustainability' in Thermodynamics remains relevant. On the basis of one single axiom: resource consumption of any kind can be quantified solely in terms of exergy flows, we demonstrate that for sufficiently complex systems certain thresholds - in terms of system's parameters - appear, below or beyond which the system exhibits an ability to remain in a self-preserving (sustainable) state. The analysis leads to non-trivial solutions in phase space, and some schematic examples are discussed in the paper: the results show a trend that seems to deserve further consideration.