Symmetry and control in thermodynamics

We explore the relationship between symmetry and entropy, distinguishing between symmetries of state and dynamical symmetries, and in the context of quantum thermodynamics between symmetries of pure and mixed states. Ultimately, we will argue that symmetry in thermodynamics is best understood as a means of control within the control theory paradigm, and we will describe an interesting technological application of symmetry-based control in the context of a quantum coherence capacitor. Symmetry, the concept from which Noether derived the conservation laws of physics, is one of the most important guiding principles of modern physics. Moreover, symmetry is often regarded as a form of order, and entropy is sometimes regarded as a measure of disorder, so it is natural to suppose that symmetry and entropy are related in some way. In this article, we will explore the relationship between symmetry and entropy, demonstrating that this relationship is by no means a simple one: in particular, it is important to distinguish between symmetries of state and dynamical symmetries, and in the context of quantum thermodynamics to distinguish between symmetries of pure and mixed states. Ultimately, we will argue that symmetry in thermodynamics is best understood as a means of control within the control theory paradigm, and we will describe an interesting technological application of symmetry-based control in the context of a quantum coherence capacitor.