The Department of Applied Mathematics weekly seminar is given by scholars and researchers working in applied mathematics, broadly interpreted.
Title: The Physics of Data, or the Entropy Theory of Information
Abstract: In classical applied mathematics, the concept of "observables" and "measurements" play very limited roles; they are the focus of statistics. Counting ad infinitum is the holographic observable to an ergodic dynamics with finite states under independent repeated sampling. Entropy provides the infinitesimal probability for an observed frequency ν w.r.t. a probability prior p. Following Callen's thermodynamic postulate and through Legendre-Fenchel transform, without help from mechanics, we show an internal energy μ emerges; it provides a linear representation of real-valued observables with full or partial information. Gibbs' fundamental thermodynamic relation and theory of ensembles follow mathematically. μ is to ν what ω is to t in Fourier analysis.