Font Size: 

Systems evolving toward an equilibrium state can be investigated looking at the energy landscape. It is well known, in fact, that their evolution approaches a minimum of the free energy, that is a maximum of the entropy of the system under a set of constraints. However, the vast majority of the systems we observe in Nature exchange energy and matter with the surroundings, thus producing entropy at the macroscopic level, and operating out of equilibrium. Then, the natural question would be: is life poised at optimizing some non-equilibrium features? The answer is much debated and far from being resolved. In this work, we propose an energy landscape approach, similar to the one commonly used at equilibrium, to a broad class of discrete-state non-equilibrium systems: the reaction networks. The stationary state can be found as the extremum of a generalized non-equilibrium potential. We present some simple examples and discuss the close-to-equilibrium limit, reminiscent of the Prigogine's principle. In the end, some new perspectives are presented, both on a possible application to diffusive systems, and on the existence of peculiar topologies which optimize energy dissipation.