Thermal Quantum Spacetime

Abstract

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

Thermofield Double States in Group Field Theory

“…The algebraic KMS Gibbs state is of course not the only equilibrium state in GFT. The maximal entropy principle gives the generalized Gibbs states of GFT [10,28], which allows a formulation of statistical field theory of quantum polyhedra. In this respect, it is promising to investigate the thermal field theories in the context of GFT.…”

“…Nevertheless, recently in [29] the equilibrium Gibbs states for GFT are constructed by the methods that do not explicitly use the pure-gravity Hamiltonian. One of the methods is Jaynes' maximum entropy principle for constrained systems, which is further used in [10,28] to study the generalized Gibbs states and background-independent statistical mechanics of quantum tetrahedra. The other method is based on the operator-algebraic Kubo-Martin-Schwinger (KMS) condition [22] and the algebraic formulation of GFT mentioned above.…”

Editorial for the Special Issue “Progress in Group Field Theory and Related Quantum Gravity Formalisms”

“…• In Thermal Quantum Spacetime [26], Isha Kotecha discusses an extension of equilibrium statistical mechanics and thermodynamics to background-independent systems that is then applied to discrete quantum gravity approaches such as GFT. A generalised notion of Gibbs equilibrium is characterised in information-theoretic terms, where entropy plays a more fundamental role than energy.…”

Beyond General Relativity: Models for Quantum Gravity, Loop Quantum Cosmology and Black Holes

“…Another interesting article in Universe deals with a thermodynamical background-independent approach to quantum space time, the "thermal quantum space time" [6]. An extension of equilibrium statistical mechanics and thermodynamics is presented, based on information-theoretic characterization of (Gibbs) thermodynamic equilibrium, which is an observer-dependent notion.…”

“…Having discussed a potential thermodynamical origin of time in [6], I move next to discuss another inspiring publication of Universe [8], which views time in cosmology as a quantum observable, not commuting with other quantum operators that define the cosmological states, such as the cosmological constant Λ. Such a "cosmological-constant-time non-commutativity" may be seen as providing a sort of uncertainty relation, which would imply that a Universe with a precise value of Λ is completely delocalized in time, i.e., the Universe in that case "does not know the time".…”