Udemy - Quantum Decoherence & Gravity from Quantum Entropy

What you'll learn
Learn how decoherence is related to the transition from the quantum to the classical world
Define the density matrix and its connection with decoherence, as well as the Von Neumann equation
Write down the density matrix for general mixed states
Learn how Quantum Entropy naturally arises from the density matrix, and how it is related to the definition of entropy in statistical mechanics
Write down the Wigner function, and learn how it is an extension of classical probabilities
Understand the Moyal equation, which is the dynamical equation satisfied by the Wigner function, and study its classical limit
Understand a recent research paper written by a mathematical physicist: Ginestra Bianconi. This paper will be the key to investigating gravity, quantum entropy.
Define eigenvalues and the logarithm of tensors
Learn the connection between Lagrangian densities and the entropic action in Ginestra Bianconi's article
Learn the generalization of the Klein Gordon equation from the quantum entropic action
Understand Topological fields, metric between vectors and bivectors
Define and learn the intuition behind the Codifferential and Dirac operator (differential forms will be used. There is also an appendix dedicated to them)
Learn the the G-field and the Θ-Field, which are used in Ginestra Bianconi's article to derive modified Einstein field equations
Derive the the cosmological constant from modified gravity
Take the variation of the entropic action to derived modified Einstein field equations
Understand how to caclulate the entropy of a black hole
Requirements
Differential forms (these will be necessary for the second part of the course. However, there is a full appendix dedicated to them)
The formalism of quantum physics (operators, observables, bra-ket notation, Hermiticity, etc). However, there is a preliminary section which serves as a refresher on the formalism of quantum mechanics. It might be consulted by those students who need to review a few concepts.
Classical field theory
Linear algebra
Classical General Relativity (the mathematics of tensors)
Description
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
Who this course is for
Advanced Physics Students: Learners pursuing upper-level undergraduate or graduate studies in physics who want to deepen their understanding of quantum decoherence, entropy, and foundational quantum theory.
Researchers and Academics: Individuals involved in theoretical or mathematical physics who are interested in modern approaches to quantum-classical transition and the role of entropy in gravitational frameworks.
Curious Enthusiasts in Quantum Foundations: Passionate learners with a strong grasp of quantum mechanics who wish to explore deeper ideas such as the Wigner function, density matrices, and the emergence of classicali behavior from quantum behavior
Those Exploring Entropic Gravity and Modified Theories: Physicists or mathematically inclined learners interested in cutting-edge theories connecting quantum information, entropy, and gravity - including Ginestra Bianconi's work on deriving gravity from entropic principles.
In summary, this course is intended for advanced physics students, researchers, and enthusiasts with a solid background in quantum mechanics and mathematical physics. It is ideal for those interested in the foundational aspects of quantum theory, the transition to classical behavior via decoherence, and the emerging connections between entropy and gravitational dynamics. The course will also benefit learners curious about modern theoretical frameworks, such as entropic gravity and modifications to Einstein's field equations.
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