Effective entropy of quantum fields coupled with gravity
Xiaoliang Qi, Stanford University
I will propose a generalisation of the quantum field theory entanglement entropy by including dynamical gravity. The generalised quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a gravitational path integral on replica geometry with a co-dimension-2 brane at the boundary of region we are studying. These results generalise the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. I'll discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries.
Barbara Terhal, TU Delft
Stephanie Wehner, TU Delft
Physics offers countless examples for which theoretical predictions are astonishingly powerful, such as the first detection of gravitational waves using near-atomic scale deformations in kilometer-scale interferometers. Unfortunately, it’s hard to imagine similar precision in complex systems, including life. The number and interdependencies between components of complex systems simply prohibits a first-principles approach: look no further than the challenge of the billions of neurons and trillions of connections within our own brains. Faced with such complexity how do we even compare theory and experiment? Here we describe an alternative, systems-scale perspective in which we integrate information theory, dynamical systems and statistical physics to extract understanding directly from measurements. We demonstrate our perspective first with a reconstructed state space of the behavior of the nematode worm C. elegans, revealing a low-dimensional chaotic attractor with symmetric Lyapunov spectrum. We then outline a maximally predictive, coarse-graining in which nonlinearities are subsumed into a linear, ensemble evolution to obtain a simple yet accurate model on multiple scales. We demonstrate this approach by identifying long timescales and collective states in the Langevin dynamics of a double-well potential and the Lorenz system. Our ``inverse’' perspective provides an emergent, quantitative framework in which to seek rather than impose effective organizing principles of complex systems.
Greg Stephens, Vrije Universiteit Amsterdam