Dealing with Uncertainty
i. To explain that as scientists we almost always only have incomplete knowledge of a system, and that this forces use to use the theory of probability; examples are: we usually do not know the microscopic state a system such as a gas or semiconductor is in, and we are often unable to measure a physical variable, such as radioisotope lifetime, very accurately;
ii. To demonstrate that we need quantitative tools, such as the Central Limit Theorem of statistics and Bayes’ theorem, to enable us, not only get the maximum understanding from the data we do have, but to quantify the uncertainty that remains;
Applications of Statistical Physics
i. To introduce the statistical physics of phase transitions, by showing how the interactions between spins in the Ising model cause the paramagnettoferromagnet phase transition. Also, the fundamental relation between fluctuations and thermodynamic functions, such as heat capacities, will be demonstrated;
ii. To introduce simple timedependent statistical processes such as diffusion in a gas, and to show how statistical physics relates microscopic phenomena such as the random motion of molecules to thermodynamic phenomena such as an increase in entropy;
iii. To show how fluctuations limit the accuracy with which experiments can measure some properties, with an application to experiments on the limits to human night vision;
iv. To introduce the basics of nanomotors. These are machines only approx. 10nm across, and so are small enough to diffuse. Nevertheless they expend energy and in doing so perform mechanical work and move in a directed fashion;
