Quantum Decoherence & Gravity from Quantum Entropy

In this course we explore the connection between entropy, quantum mechanics, and gravity. In this advanced theoretical physics course, we examine the fundamental role of quantum decoherence in the transition from quantum to classical behavior, and we intrpduce the concept of quantum entropy (this will be the first part of the course). After that, we take a step forward, investigating how gravity itself may emerge from entropic principles.

Starting from the density matrix formalism, we develop a clear understanding of decoherence and how it explains the classical appearance of a fundamentally quantum world. We also analyze the important concept of Wigner function, which serves as a tool for connecting quantum dynamics with classical phase space. Then, we rigorously define quantum entropy, using the Von Neumann formulation.

In the second half of the course, we apply these tools to modern research topics. We explore topological metrics, codifferential operators, and the variation of entropic actions. Special emphasis is placed on a recent and influential work by Ginestra Bianconi, which derives modified Einstein field equations using entropy as a fundamental physical quantity.

This course integrates insights from quantum physics, general relativity, field theory, differential forms, and information theory, making it suitable for physicists, mathematicians, and engineers interested in the cutting-edge theoretical landscape. What You'll LearnHow to describe decoherence using the density matrix and von Neumann equationThe role of the Wigner function in bridging classical and quantum dynamicsThe concept and computation of quantum entropyHow entropy can lead to entropic actions for matter and gauge fieldsThe structure and variation of topological and geometrical actionsA detailed walkthrough of Ginestra Bianconi's paper "Gravity from Entropy"Derivation of modified Einstein equations from entropic considerationsThe emergence of a cosmological constant from an entropic actionHow to calculate the (quantum) entropy of a blackhole (by analyzing another article written by Ginestra Bianconi)Who Is This Course For. Physicists and mathematicians interested in quantum gravity or foundations of quantum theoryResearchers or students in theoretical physics, mathematical physics, or complex systemsAnyone curious about how information and entropy may be fundamental to space, time, and gravity.