A Pedagogical Introduction of Full Counting Statistics in the Context of Quantum Thermodynamics and Quantum Noise

This tutorial presents an illustrative overview behind the idea of the two time mea- surement protocol scheme in connection with the method of Full Counting Statistics, a widely used tool in the context of Quantum Thermodynamics and quantum noises. This article presents the mathematical tools to derive the quantum master equation for the de- formed reduced density operator for the system in the most general way by tracing out the bath degrees of freedom for different types of interaction Hamiltonians generally used to model the open quantum system problems in the limit of weak system bath coupling. The derivation of the microscopic Q.M.E has also been described. Finally, the article provides an application of the Full counting statistics method for the well known Resonant Level Model of thermoelectric transport and its connection with the Fluctuation symmetry.