A thermodynamical study of the clockwork hypothesis proposed by E. Schrödinger

In the present study, the 'clockwork' hypothesis proposed by Schrödinger was examined from the viewpoint of thermodynamics. Firstly, noticing a unidirectional transfer of entropy in a heat engine, the logic was briefly explained about a close relation between this entropy transfer and an irreversible cycle performed by a working body. Next, paying attention to two fundamental differences between a heat engine and a biological system, we considered an isolated system Asigma consisting of three one-component systems (Ai, A, Ao) and noted a case that the same molecules as the component ones flowed quasistatically into Ai from the outside. Then, the unidirectional flows of the molecules, energy and entropy, which were induced by the above inflow in Asigma, were formulated on the basis of the equilibrium thermodynamics for an open system. Furthermore, it was clarified that the fundamental equation for these flows is the Schrödinger inequality and that the necessary-sufficient condition for this inequality is the existence of an irreversible cycle performed by A. Here A corresponds to a working body in a heat engine. It was, thus, concluded that the 'clockwork' hypothesis by Schrödinger is considered to be reasonable for a biological system composed of various irreversible subsystems.