Free energies

Free energies ignore most of a system, to provide the emergent statistical ensemble describing things we care about. Free energies can ignore the external world. The cost of borrowing energy from the world is measured by the temperature, giving us the canonical ensemble and Helmholtz free energy. Similarly, borrowing particles and volume from the world gives us the grand canonical and Gibbs ensembles. Free energies can ignore unimportant internal degrees of freedom. These lead to friction and noise, and theories of chemical reactions and reaction rates. Free energies can be coarse-grained, removing short distances and times. Exercises apply free energies to molecular motors, thermodynamic relations, reaction rate theory, Zipf’s law for word frequencies, zombie outbreaks, and nucleosynthesis.