Sustainable Efficiency of Far-from-equilibrium Systems

The Carnot efficiency of usual thermal motors compares the work produced by the motor to the heat received from the hot source, neglecting the perturbation of the cold source: thus, even if it may be appropriate for industrial purposes, it is not pertinent in the scope of sustainable development and environment care. In the framework of stochastic dynamics we propose a different definition of efficiency, which takes into account the entropy production in all the irreversible processes considered and allows for a fair estimation of the global costs of energy production from heat sources: thus, we may call it "sustainable efficiency". It can be defined for any number of sources and any kind of reservoir, and it may be extended to other fields than conventional thermodynamics, such as biology and, hopefully, economics. Both sustainable efficiency and Carnot efficiency reach their maximum value when the processes are reversible, but then, power production vanishes. In practise, it is important to consider these efficiencies out of equilibrium, in the conditions of maximum power production. It can be proved that in these conditions, the sustainable efficiency has a universal upper bound, and that the power loss due to irreversibility is at less equal to the power delivered to the mechanical, external system. However, it may be difficult to deduce the sustainable efficiency from experimental observations, whereas Carnot's efficiency is easily measurable and most generally used for practical purposes. It can be shown that the upper bound of sustainable efficiency implies a new higher bound of Carnot efficiency at maximum power, which is higher than the so-called Curzon-Ahlborn bound of efficiency at maximum power.