Energy Fluctuations In Thermally Isolated Driven Systems

Abstract

This thesis presents a theoretical review of systems that are thermally isolated and are under the action of some external protocol or drive. Here we have discussed these systems by for mulating a Fluctuation-Dissipation relation appropriately describing their physics. Firstly, we have derived the Fluctuation-Dissipa tion relation using the Fokker-Planck equation and then by using Quantum Crooks equality leading to an expression for the energy fluctuations in the system of interest. We have shown in detail that energy fluctuations in thermally isolated sys tems that are driven away from equilibrium by some external parameter are universal in nature and follow a non-Gibbsian pattern. 'vVe have predicted that there exist two different regimes with a continuous second-order-like transition between them. We have explicitly shown two distinct regimes depending on the value of order parameter 7] i.e., Gibb 's like behaviour for (7] < 1) and run away like for (7] > 1). We have verified our approach by applying it to both interacting and non-interacting systems.