Exploring the entropy concept for coupled oscillators

The purpose of this paper is to explore the concept of mixing entropy for systems of coupled harmonic oscillators. First, entropy is examined theoretically for a generalized oscillator configuration. A general formulation for the mixing entropy is obtained by comparing the actual entropy of a system to its hypothetical decoupled entropy. It is proven that the mixing entropy of any system is nonnegative, and that the entropy inequality property reduces to an equality with the introduction of a mixing entropy term. This result is validated using a series of numerical examples, which provide insight into the relationship between energy and entropy behavior. First, the mixing entropy is examined for an undamped system of two identical coupled oscillators. The same methodology is then applied for a system of nonidentical oscillators. Lastly, the mixing entropy is determined for a system composed of a main oscillator attached to a fuzzy structure.