Abstract
The first lecture was mainly devoted to an introduction to non-equilibrium systems and reminders, such as the macroscopic definition of entropy in thermodynamics. This definition is based on the following postulates:
- Entropy is only defined for systems at equilibrium;
- Entropy is a state function: it does not depend on the history of the system, but only on the macroscopic variables that characterize it;
- Entropy is additive;
- During any transformation, the entropy of an isolated system can only increase. It remains constant when the transformation is reversible;
- The entropy of a thermostat is proportional to its energy, and the proportionality coefficient defines the thermostat's temperature.
A priori, these postulates only allow us to define the entropy of thermostats. The entropy of any system at equilibrium is derived by carrying out reversible transformations, and writing that, during these transformations, the sum of the change in entropy of the system and that of the thermostats is zero. In this way, we can rediscover the classic results of thermodynamics relating to the second principle, such as Clausius' inequality, Carnot's bound on the efficiency of a thermal machine or the impossibility of perpetual motion. This purely thermodynamic point of view cannot be generalized to non-equilibrium systems, even in a stationary regime, and there is no macroscopic definition of entropy. A corollary is that, in a stationary non-equilibrium regime, unlike equilibrium, thermodynamic forces no longer derive from a potential.
