Abstract
Abstract When a chain wriggles on a plate vibrated vertically by a speaker, its behavior is similar to that of a polymer in a solution. Since the former is far from equilibrium, it is doubtful to coin the concept of a temperature, which is determined by the heat bath a polymer solution comes into contact with. Some energy scale is clearly required to describe the vigor of the chain motion. Then, how does this scale depends on the frequency and amplitude（f/A）of the speaker? In the end, two experiments on entropic force are designed and discussed to tackle the nature of this energy scale. Because our chain is of finite steps and the neighboring steps are constrained with a maximum bending angle, we use both numerical simulation and model-building in our theoretical analysis. The main conclusions are: i) By taking into account the fact that there is a maximum height a chain can jump, f/A of the speaker can affect the distribution function, p(r), of the end-to-end distance of our chain. It is equivalent to placing a totally-reflecting plate above the chain, which enables us to use the image method. ii) Since the digital video has a finite lens, discarding of the images whose end points move outside of the scope introduces a bias to the distribution function. iii) Resonances appear in most of the f/A ranges. When they occur, p(r) becomes much narrower with its peak moving toward larger r values. All the three above properties imply that the f/A of the speaker comes into the problem in a subtler way than a simple characteristic energy scale. When partial segments of a polymer are confined within two walls, it will experience an entropic force due to the different entropies. This is also observed for our chain. Since there is a dispute over the concept of temperature, we construct another experiment to clarify it. Part of the plate is covered with soft material such that more energy is lost during each collision. We simulate those segments over it as experiencing lower “temperature”. Since neither parts of the chain is confined, the entropic force comes from the different energies they experience. Is the energy of a chain the same as the thermodynamic temperature? We preliminarily expect the average energy of the chain to play such a role.