Fluctuation theorem, nonequilibrium work, and molecular machines

We could paraphrase Professor Noyori [1] and say that the science of molecular machines is four-dimensional chemistry since their 3D structure (x, y, z) is coupled to their motion and kinetics (t). In condensed phases at equilibrium, the motion is erratic with equal probabilities of moving forward or backward according to the principle of detailed balance. Therefore, unidirectional motion is possible if the machine is driven out of equilibrium by some chemical, electrochemical, electronic, or photonic energy source [2–7]. In performing the conversion of energy into motion, the molecular machine is the stage of dissipative processes taking place at the nanoscale in the presence of thermal fluctuations. Accordingly, molecular machines are ruled not only by the laws of thermodynamics but also by the statistical laws of fluctuations ubiquitous at the nanoscale. Remarkably, major results have been recently discovered which combine the thermodynamic and statistical laws into general relationships valid in nonequilibrium nanosystems such as molecular machines. Our purpose is here to give a brief summary of these new results which are called fluctuation theorems and nonequilibrium work relations, and to illustrate their application to the F1-ATPase molecular motor.