Non-equilibrium thermodynamics of magnetic resonance using the quantum mechanics

In this paper we give a pedagogical introduction to non-equilibrium thermodynamics of small quantum systems, using only basic concepts from undergraduate quantum and statistical mechanics. After reviewing the concept of work, as usually taught in thermodynamics and statistical mechanics, we discuss the framework of non-equilibrium processes in quantum systems together with some modern developments, such as the Jarzynski equality and its connection to the second law of thermodynamics. We then apply these results to the problem of magnetic resonance, where all calculations may be done exactly. It is shown in detail how to build the statistics of the work, both for a single particle and for a collection of non-interacting particles. We hope that this paper may serve as a tool to bring the new student up to date on the recent developments in non-equilibrium thermodynamics.