Explore the fascinating world of entropy, order, and disorder in this comprehensive lecture by renowned physicist Daan Frenkel from the University of Cambridge. Delve into the shifting perspectives on entropy as a measure of disorder since the mid-20th century, examining intriguing examples where entropy increases with increasing order. Gain insights into Gibbs' paradox and discover how recent numerical tools allow for the computation of close and distant relatives of Boltzmann's entropy. Journey through topics such as thermodynamics, hard-sphere liquids, entropic ordering in complex structures, and the relationship between entropy and granular materials. Learn about the challenges in counting distinct jammed states, the strange nature of high-dimensional basins, and the applications of these concepts in materials discovery and deep neural networks. Engage with thought-provoking discussions on Gibbs' statistical mechanics, the treatment of identical particles, and the Edwards hypothesis in granular systems. Read more