Fluctuations relations of equilibrium states with broken symmetry
It is a general rule that as a system gets smaller its fluctuations increase. As a consequence, in small systems thermodynamic quantities like work or heat are only defined in a statistical sense. Exact relations between the statistical distributions of thermodynamic quantities, known as fluctuations relations, have been discovered about two decades ago. These relations provide a direct way to measure irreversibility in non-equilibrium systems, from the degree by which time-reversal symmetry is broken.
One may wonder whether such fluctuation relations would hold for more general broken symmetries even in equilibrium systems. In this presentation, we will argue that indeed whenever a symmetry is broken by an external field, the probabilitydistribution of the order parameter also obeys a specific fluctuation relation, which remarkably holds already for finite systems . In the thermodynamic limit, we will discuss consequences of the relation for spontaneous symmetry breaking.
In a second part, I will try to present briefly a different study, mostly pedagogical, on the trajectory thermodynamics of a tagged particle within an harmonic chain subject to a time dependent force .