Equilibrium Chemical Engines

The molecular machine in biological systems works as a chemical energy transducer. For instance, the protein motors such as myosin and kinesins, or flagellar motor produce mechanical energy as they consume the chemical energy provided by hydrolysis of ATP or proton density gradient. Some other proteins, such as enzymes or pump proteins of membrane transportation, can be also thought as chemical energy transducer in which energy input and output are both chemical. Recently various phenomenological models for protein motors have been studied and the thermodynamic interpretation for these models have been presented. 5) However, the models, in which chemical reaction is taken into account, are scarcely proposed. While the energetics of models, in which chemical reaction is explicitly supposed, may be future task, none have discussed an equilibrium cycle associated with any chemical reaction, as Carnot considered Carnot cycle for thermal energy transduction. Also the notion of energy transduction efficiency from chemical to mechanical has never been stated explicitly. These will be important when we compare the energy transduction in molecular machines with macroscopic thermodynamics. In this Paper, we discuss how we should define a proper chemical energy transduction efficiency and how we construct an engine which gives its maximal value. In §2, a chemical engine to transduce energy of arbitrary chemical reaction into mechanical energy is proposed. In §3, we review the chemical thermodynamics of the processes involving the chemical reaction. Equilibrium chemical reaction is also presented. In §4 and §5, we show an equilibrium reversible cycle using the chemical engine as to correspond to the idealized cycle for heat engines which Carnot considered. Further we propose efficiency for chemical energy transduction, and show its maximum value. In §6, the heat flow associating with particle flow is studied. In §7, we study some applications to compare energetic behavior of molecular engines with macroscopic