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 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.
Highlights
Background independence is a hallmark of general relativity that has revolutionised our conception of space and time
This emergence in quantum gravity is akin to that in condensed matter systems in which coarse-grained macroscopic properties of the physical systems are extracted from the microscopic dynamical theories of the constituent atoms. In this sense our universe can be understood as an unusual condensed matter system, brought into the existing smooth geometric form by a phase transition of a quantum gravity system of pre-geometric ‘atoms’ of space; in particular, as a condensate [9]. This brings our motivations full circle, and to the core of this article: to illustrate, the potential of and preliminary evidence for, a rewarding exchange between a background independent generalisation of statistical mechanics and discrete quantum gravity; and show that ideas from the former are vital to investigate statistical mechanics and thermodynamics of quantum gravity, and that its considerations in the latter could in turn provide valuable insights into the former
Equilibrium states are a cornerstone of statistical mechanics, which in turn is the theoretical basis for thermodynamics
Summary
Background independence is a hallmark of general relativity that has revolutionised our conception of space and time. In this sense our universe can be understood as an unusual condensed matter system, brought into the existing smooth geometric form by a phase transition of a quantum gravity system of pre-geometric ‘atoms’ of space; in particular, as a condensate [9] This brings our motivations full circle, and to the core of this article: to illustrate, the potential of and preliminary evidence for, a rewarding exchange between a background independent generalisation of statistical mechanics and discrete quantum gravity; and show that ideas from the former are vital to investigate statistical mechanics and thermodynamics of quantum gravity, and that its considerations in the latter could in turn provide valuable insights into the former.
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