Physical aging is an active subject in statistical physics as it could lead to the generalization of equilibrium statistical physics to weakly out of equilibrium systems. In this context, where polymers and spin glasses have already been extensively studied despite not still well understood, theoretical works have shown new interests in systems undergoing a second order phase transition, where model ingredients are based on simpler physical arguments. Therefore, we studied in details a second order phase transition in liquid crystals : the Fréedericksz transition, in order to monitor experimentally aging at its critical point. We showed that the equations usually proposed to describe the dynamics of the transition (Landau like development of the free energy) have a very limited domain of validity, not accessible experimentally. In fact, one has to take into account the non-linearities, even in the vicinity of the Fréedericksz threshold and in the linear response regime. In this framework, we found a very good agreement between numerical simulations (no adjustable parameters) and experimental results. Then, we studied the behavior of fluctuations in the vicinity of the transition threshold and showed that, when ones takes into account the quadratic dependence of the measured variable, the fluctuations have a maximal amplitude at the threshold, as expected in a second order phase transition. This experimental study of fluctuations provides a new method to precisely measure of the value of the Fréedericksz threshold. A detailed analysis of the system dynamic fluctuations during quenches, and in particular, critical quenches was also performed, and we found the same behavior as predicted on spin glasses. The relation between fluctuation-dissipation theorem violation and variance evolution during the quench could be established. In parallel, we designed an experimental set-up to study the spatio-temporal fluctuations and also used a classical one, which both have sensitivity limits due to the mean value of the order parameter. We therefore propose a third set-up which could not be implemented due to a lack of time, that should overcome these difficulties.
