8 research outputs found
Statistical Equilibrium in Quantum Gravity: Gibbs states in Group Field Theory
Gibbs states are known to play a crucial role in the statistical description
of a system with a large number of degrees of freedom. They are expected to be
vital also in a quantum gravitational system with many underlying fundamental
discrete degrees of freedom. However, due to the absence of well-defined
concepts of time and energy in background independent settings, formulating
statistical equilibrium in such cases is an open issue. This is even more so in
a quantum gravity context that is not based on any of the usual spacetime
structures, but on non-spatiotemporal degrees of freedom. In this paper, after
having clarified general notions of statistical equilibrium, on which two
different construction procedures for Gibbs states can be based, we focus on
the group field theory formalism for quantum gravity, whose technical features
prove advantageous to the task. We use the operator formulation of group field
theory to define its statistical mechanical framework, based on which we
construct three concrete examples of Gibbs states. The first is a Gibbs state
with respect to a geometric volume operator, which is shown to support
condensation to a low-spin phase. This state is not based on a pre-defined
symmetry of the system and its construction is via Jaynes' entropy maximisation
principle. The second are Gibbs states encoding structural equilibrium with
respect to internal translations on the GFT base manifold, and defined via the
KMS condition. The third are Gibbs states encoding relational equilibrium with
respect to a clock Hamiltonian, obtained by deparametrization with respect to
coupled scalar matter fields.Comment: v2 31 pages; typos corrected; section 2 modified substantially for
clarity; minor modifications in the abstract and introduction; arguments and
results unchange
Statistical equilibrium of tetrahedra from maximum entropy principle
Discrete formulations of (quantum) gravity in four spacetime dimensions build
space out of tetrahedra. We investigate a statistical mechanical system of
tetrahedra from a many-body point of view based on non-local, combinatorial
gluing constraints that are modelled as multi-particle interactions. We focus
on Gibbs equilibrium states, constructed using Jaynes' principle of constrained
maximisation of entropy, which has been shown recently to play an important
role in characterising equilibrium in background independent systems. We apply
this principle first to classical systems of many tetrahedra using different
examples of geometrically motivated constraints. Then for a system of quantum
tetrahedra, we show that the quantum statistical partition function of a Gibbs
state with respect to some constraint operator can be reinterpreted as a
partition function for a quantum field theory of tetrahedra, taking the form of
a group field theory.Comment: v3 published version; v2 18 pages, 4 figures, improved text in
sections IIIC & IVB, minor changes elsewher
Statistical equilibrium in quantum gravity: Gibbs states in group field theory
Gibbs states are known to play a crucial role in the statistical description of a system with a large number of degrees of freedom. They are expected to be vital also in a quantum gravitational system with many underlying fundamental discrete degrees of freedom. However, due to the absence of well-defined concepts of time and energy in background independent settings, formulating statistical equilibrium in such cases is an open issue. This is even more so in a quantum gravity context that is not based on any of the usual spacetime structures, but on non-spatiotemporal degrees of freedom. In this paper, after having clarified general notions of statistical equilibrium, on which two different construction procedures for Gibbs states can be based, we focus on the group field theory (GFT) formalism for quantum gravity, whose technical features prove advantageous to the task. We use the operator formulation of GFT to define its statistical mechanical framework, based on which we construct three concrete examples of Gibbs states. The first is a Gibbs state with respect to a geometric volume operator, which is shown to support condensation to a low-spin phase. This state is not based on a pre-defined symmetry of the system and its construction is via Jaynes’ entropy maximisation principle. The second are Gibbs states encoding structural equilibrium with respect to internal translations on the GFT base manifold, and defined via the KMS condition. The third are Gibbs states encoding relational equilibrium with respect to a clock Hamiltonian, obtained by deparametrization with respect to coupled scalar matter fields.Deutscher Akademischer Austauschdienst https://doi.org/10.13039/501100001655Peer Reviewe
Quantum Frame Relativity of Subsystems, Correlations and Thermodynamics
It was recently noted that different internal quantum reference frames (QRFs)
partition a system in different ways into subsystems, much like different
inertial observers in special relativity decompose spacetime in different ways
into space and time. Here we expand on this QRF relativity of subsystems and
elucidate that it is the source of all novel QRF dependent effects, just like
the relativity of simultaneity is the origin of all characteristic special
relativistic phenomena. We show that subsystem relativity, in fact, also arises
in special relativity with internal frames and, by implying the relativity of
simultaneity, constitutes a generalisation of it. Physical consequences of the
QRF relativity of subsystems, which we explore here systematically, and the
relativity of simultaneity may thus be seen in similar light. We focus on
investigating when and how subsystem correlations and entropies, interactions
and types of dynamics (open vs. closed), as well as quantum thermodynamical
processes change under QRF transformations. We show that thermal equilibrium is
generically QRF relative and find that, remarkably, . We further examine how
non-equilibrium notions of heat and work exchange, as well as entropy
production and flow depend on the QRF. Along the way, we develop the first
study of how reduced subsystem states transform under QRF changes. Focusing on
physical insights, we restrict to ideal QRFs associated with finite abelian
groups. Besides being conducive to rigour, the ensuing finite-dimensional
setting is where quantum information-theoretic quantities and quantum
thermodynamics are best developed. We anticipate, however, that our results
extend qualitatively to more general groups and frames, and even to subsystems
in gauge theory and gravity.Comment: 49 pages + appendices, 12 figures. Comments welcom
Machine learning for cognitive behavioral analysis: datasets, methods, paradigms, and research directions
Abstract Human behaviour reflects cognitive abilities. Human cognition is fundamentally linked to the different experiences or characteristics of consciousness/emotions, such as joy, grief, anger, etc., which assists in effective communication with others. Detection and differentiation between thoughts, feelings, and behaviours are paramount in learning to control our emotions and respond more effectively in stressful circumstances. The ability to perceive, analyse, process, interpret, remember, and retrieve information while making judgments to respond correctly is referred to as Cognitive Behavior. After making a significant mark in emotion analysis, deception detection is one of the key areas to connect human behaviour, mainly in the forensic domain. Detection of lies, deception, malicious intent, abnormal behaviour, emotions, stress, etc., have significant roles in advanced stages of behavioral science. Artificial Intelligence and Machine learning (AI/ML) has helped a great deal in pattern recognition, data extraction and analysis, and interpretations. The goal of using AI and ML in behavioral sciences is to infer human behaviour, mainly for mental health or forensic investigations. The presented work provides an extensive review of the research on cognitive behaviour analysis. A parametric study is presented based on different physical characteristics, emotional behaviours, data collection sensing mechanisms, unimodal and multimodal datasets, modelling AI/ML methods, challenges, and future research directions