Entropy production on a single trajectory of the small system

The following PowerPoint file is from the talk which I gave in my research group recently. It is also my understanding and reading notes from a serial of papers by Prof. Udo Seifert, in which he generalized the entropy production on a single trajectory of the small system such as a molecular machine. It mainly addresses three questions:

1. Just as thermodynamics was developed to calculate the energy efficiency of the macro-machine, we need to develop further the thermodynamics to solve the problem of the efficiency of the micro-machine, see Fig. 1.
2. Molecular machines in cell works differently from their counterparts in the macro-world. They take advantage of thermal noise in the micro-world to do work, which is the reason why molecular machines usually have a higher energy efficiency.
3. To deal with a small system, the second thermodynamics law is generalized to the fluctuation theorem, which means the negative entropy is possible in the single trajectory.