Quantum thermodynamics and work fluctuations with applications to magnetic resonance

Abstract

In this paper we give a pedagogical introduction to the ideas of quantum thermodynamics and work fluctuations, using only basic concepts from 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 of quantum systems.

This is a pedagogical paper

References in corpus (4)

• Fluctuation theorems: Work is not an observable
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Adiabatic processes realized with a trapped Brownian particle
• Fluctuation theorems in driven open quantum systems

Cited by in corpus (8)

• Unravelling the role of coherence in the first law of quantum thermodynamics
• Employing Non-Markovian effects to improve the performance of a quantum Otto refrigerator
• Quantum mechanical work
• Verifying detailed fluctuation relations for discrete feedback-controlled quantum dynamics
• Fluctuation theorems for genuine quantum mechanical regimes
• Two famous results of Einstein derived from the Jarzynski equality
• Thermal transport through a single trapped ion under strong laser illumination
• Realization of Trapped Ion Dynamics in the Strong-Field Regime and Non-Markovianity