The following PowerPoint file is from my talk in our 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 bio-molecules. It mainly addressed three questions:
1) Just as thermodynamics was developed to calculate the energy efficiency of the macro-machine, we need to develop further thermodynamics to calculate the efficiency of the micro-machine, such as Myosin and Kinesin:
Fig. 1 Molecular motors – Myosin and Kinesin’s walking steps on the microtubule
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.
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