Abstract
The fourth lecture was devoted to the different ways of representing thermostats by deterministic dynamics: the Berendsen thermostat, the Nosé-Hoover thermostat, the Gaussian thermostat. In each of these cases, the effect of the thermostat is to modify the Hamiltonian dynamics, by adding friction terms that keep certain quantities constant. For example, in the case of a system in contact with several thermostats, we can introduce, for each thermostat, a friction force that acts on all particles interacting with this thermostat, with the effect of keeping the total kinetic energy of these particles constant. The effect of these frictional forces is to modify Liouville's theorem. The volume of the phase space is no longer conserved over time, and its variation can be interpreted as a change in entropy. Another way of representing a thermostat is to consider it as consisting of a large number of degrees of freedom. For certain choices of the characteristics of these internal degrees of freedom, their effect can be described by a Langevin equation.
