The Second Principle of Thermodynamics is a macroscopic theory at the heart of our understanding of irreversible phenomena. At the scale of small systems, such as small biomolecules or mesoscopic conductors, it is constantly violated by fluctuations. A whole series of recent works have made it possible to predict and experimentally verify statistical properties of these fluctuations based on very general relations such as the fluctuation theorem or Jarzynski relations.
This 2015-2016 lecture, intended as an introductory course to non-equilibrium systems, attempted to take stock of these recent advances, introducing the language of large deviations. It showed how many results from non-equilibrium physics, such as fluctuation-dissipation relations or Onsager relations, can be easily understood within the framework of stochastic thermodynamics. For example, for an arbitrary Markov process, concepts such as work, heat and free energy can be defined, and all thermodynamics can be recovered by elementary calculations.
Describing non-equilibrium systems with microscopic models requires precise representation of the effect of thermostats. Whether we start from a deterministic or stochastic model of the coupling with these thermostats and the evolution of internal degrees of freedom, we must adopt a probabilistic characterization of all physical quantities relating to small systems, if only because of our lack of information on the initial condition. Within the framework of stochastic thermodynamics, this means associating the work and heat exchanged with the outside world with each microscopic trajectory, thus enabling us to establish the statistical laws satisfied by these quantities.