Generalized Gibbs Ensembles in Discrete Quantum Gravity

Chirco, Goffredo; Kotecha, Isha

doi:10.1007/978-3-030-26980-7_66

Cited by 10 publications

(14 citation statements)

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“…This brings us to the proposal of characterising a generalised Gibbs state based on a constrained maximisation of information (Shannon or von Neumann) entropy [14][15][16], along the lines advocated by Jaynes [19,20] purely from the perspective of evidential statistical inference. Jaynes' approach is fundamentally different from other more traditional ones of statistical physics.…”

Section: Thermodynamical Characterisationmentioning

confidence: 99%

“…OperatorsK andV have well-defined actions on the Fock space H F . Using the thermodynamical characterisation then, we can consider the formal constraints 16 where a = 1, 2 and the partition function 17 is,…”

Section: )mentioning

confidence: 99%

“…This issue, especially in the context of gravity, was brought to the fore in a seminal work [1], and developed subsequently in [2,3,10,11]. Valuable insights from these studies on spacetime relativistic systems [1][2][3][11][12][13] have also formed the conceptual backbone of first applications to discrete quantum gravity [14][15][16]. In this section, we present extensions of equilibrium statistical mechanics to background independent 1 systems, laying out different proposals for a generalised statistical equilibrium, but emphasising on one in particular, and based on which further aspects of a generalised thermodynamics are considered.…”

Section: Background Independent Equilibrium Statistical Mechanicsmentioning

confidence: 99%

“…More standard choices include a Hamiltonian in a non-relativistic system, a clock Hamiltonian in a deparametrized system [3,14], and generators of kinematic symmetries like rotations, or more generally of 1-parameter subgroups of Lie group actions [26,27]. Some of the more unconventional choices include geometric observables like volume [14,28], (component functions of the) momentum map associated with geometric closure of classical polyhedra [15,16], half-link gluing (or face-sharing) constraints of discrete gravity [15], a projector in group field theory [15,29], and generic gauge-invariant observables (not necessarily symmetry generators) [11]. We refer to [14] for a more detailed discussion.…”

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confidence: 99%

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Thermal Quantum Spacetime

Kotecha

2019

Universe

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The intersection of thermodynamics, quantum theory and gravity has revealed many profound insights, all the while posing new puzzles. In this article, we discuss an extension of equilibrium statistical mechanics and thermodynamics potentially compatible with a key feature of general relativity, background independence; and we subsequently use it in a candidate quantum gravity system, thus providing a preliminary formulation of a thermal quantum spacetime. Specifically, we emphasise on an information-theoretic characterisation of generalised Gibbs equilibrium that is shown to be particularly suited to background independent settings, and in which the status of entropy is elevated to being more fundamental than energy. We also shed light on its intimate connections with the thermal time hypothesis. Based on this we outline a framework for statistical mechanics of quantum gravity degrees of freedom of combinatorial and algebraic type, and apply it in several examples. In particular, we provide a quantum statistical basis for the origin of covariant group field theories, shown to arise as effective statistical field theories of the underlying quanta of space in a certain class of generalised Gibbs states. CONTENTS

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Section: Thermodynamical Characterisationmentioning

confidence: 99%

Section: )mentioning

confidence: 99%

Section: Background Independent Equilibrium Statistical Mechanicsmentioning

confidence: 99%

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confidence: 99%

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Thermal Quantum Spacetime

Kotecha

2019

Universe

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“…We can describe the same structures from a many-body perspective [19], and treat as more fundamental an in-teracting system of many such quanta. This viewpoint enables us to import formal techniques from standard many-body physics for macroscopic systems, by treating a quantum polyhedron or an open spin network node as a single atom or particle of interest [5,6,20,21]. This further leads to a modelling of an extended region of discrete quantum space (a spin network) as a multi-particle state with a large number of such quanta, and a region of dynamical quantum spacetime (a spin foam) as an interaction process.…”

Section: Introductionmentioning

confidence: 99%

Thermal representations in group field theory: squeezed vacua and quantum gravity condensates

Assanioussi¹,

Kotecha²

2020

J. High Energ. Phys.

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We apply the formalism of thermofield dynamics to group field theory quantum gravity and construct thermal representations associated with generalised equilibrium Gibbs states using Bogoliubov transformations. The newly constructed class of thermal vacua are entangled, two-mode squeezed, thermofield double states. The corresponding finite temperature representations are inequivalent to the standard zero temperature one based on a degenerate vacuum. An interesting class of states, coherent thermal states, are defined and understood as thermal quantum gravity condensates.

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Multi-symplectic Lie Group Thermodynamics for Covariant Field Theories

Chirco

Laudato

Mele

2019

Lecture Notes in Computer Science

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Inspired by Souriau's symplectic generalization of the Maxwell-Boltzmann-Gibbs equilibrium in Lie group thermodynamics, we investigate a spacetime-covariant formalism for statistical mechanics and thermodynamics in the multi-symplectic framework for relativistic field theories. A general-covariant Gibbs state is derived, via a maximal entropy principle approach, in terms of the covariant momentum map associated with the lifted action of the diffeomorphisms group on the extended phase space of the fields. Such an equilibrium distribution induces a canonical spacetime foliation, with a Lie algebra-valued generalized notion of temperature associated to the covariant choice of a reference frame, and it describes a system of fields allowed to have non-vanishing probabilities of occupying states different from the diffeomorphism invariant configuration. We focus on the case of parametrized first order field theories, as a concrete simplified model for fully constrained field theories sharing fundamental general covariant features with canonical general relativity. In this setting, we investigate how physical equilibrium, hence time evolution, emerge from such a state via a gauge-fixing of the diffeomorphism symmetry.

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Generalized Gibbs Ensembles in Discrete Quantum Gravity

Cited by 10 publications

References 10 publications

Thermal Quantum Spacetime

Thermal Quantum Spacetime

Thermal representations in group field theory: squeezed vacua and quantum gravity condensates

Multi-symplectic Lie Group Thermodynamics for Covariant Field Theories

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