Configurational entropy of confined Wigner clusters

Complete text of publication follows. Competition between the strong repulsion between charged particles and their external confinement results in formation of ordered structures -Wigner clusters. A number of informative experiments have been performed on charged particles in a plasma environment, however, the phenomenon is a general one as analogous situations exist in diverse systems such as semiconductor quantum dots or vortex matter in superconductors. In most cases, a number of competing stable configurations (the ground state plus numerous metastable states) are observed. It is often argued that the total number of metastable states grows exponentially with the the number of particles in the trap. However, the total number of metastable states is not a well-defined and representative quantity as different states have very different realization probabilities, and not all metastable states are found during the finite time of an experiment or a simulation. Therefore we propose to rely on an alternative concept of configurational entropy [3] akin to the Shannon entropy defined in the context of information theory: S = -Σkpk log pk. Here, the index k numbers various stable configurations and pk stands for their respective realization probabilities. This entropy may be understood as the logarithm of the effective number of states. We apply the concept of configurational entropy to confined 2D and 3D systems interacting through both long-range (Coulomb) and short-range (Yukawa, logarithmic) forces. The results indicate that: (i) the entropy is indeed a robust quantity as it can be determined quickly and reliably, (ii) the entropy is larger in systems with short interparticle interaction range, and (iii) the effective number of states grows faster than the exponential function of the number of constituent particles.