arXiv subjects

Antoine Rignon-Bret

Publications and source records attributed to Antoine Rignon-Bret.

14 recordsLinked to original sources

arXiv2026

Black hole thermodynamics at null infinity. Part 1: Dual Generalized Second Law

The generalized second law (GSL) of black hole thermodynamics asserts the monotonic increase of the generalized entropy combining the black hole area and the entropy of quantum fields outside the horizon. Modern proofs of the GSL rely on information theoretic methods and are typically formulated using algebras of observables defined on the event horizon together with a vacuum state invariant under horizon symmetries, inducing a geometric modular flow. In this work, we formulate a dual version of the generalized second law from the perspective of asymptotic observers at future null infinity, who do not have access to the black hole area. Our approach exploits the dependence of the second law on the choice of algebra of observables and of a reference state invariant under suitable symmetries, in close analogy with open quantum thermodynamics. Using algebraic quantum field theory and modular theory, we analyze several physically motivated vacuum states, including the Hartle Hawking state and two classes of regularized vacua. We show that, at null infinity, the monotonic quantity governing an irreversible evolution is no longer the generalized entropy, but rather a thermodynamic potential constructed from asymptotic observables. Depending on the chosen vacuum, this potential takes the form of the free energy or of a generalized grand potential built from the Bondi mass and additional (angular) mode dependent chemical potentials. The resulting inequalities define a dual generalized second law at future null infinity, which can be consistently combined with the standard GSL involving variations of the black hole area.

hep-th↗

arXiv2026

Black hole thermodynamics at null infinity. Part 2: Open systems, Markovian dynamics and work extraction from non-rotating black holes

Black hole thermodynamics provides a unique setting in which general relativity, quantum field theory, and statistical mechanics converge. In semiclassical gravity, this interplay culminates in the generalized second law (GSL), whose modern proofs rely on information theoretic techniques applied to algebras of observables defined on null hypersurfaces. These proofs exhibit close structural parallels with the thermodynamics of open quantum systems governed by Markovian dynamics. In this work, we draw parallels between the dynamics of quantum fields in regions bounded by non expanding causal horizons and the thermodynamics of quantum systems weakly coupled to equilibrium reservoirs. We introduce a dictionary relating late time boundary conditions to the choice of reservoir, vacuum states to fixed points of the dynamics, and modular Hamiltonians to thermodynamic potentials. Building on results from a companion paper on dual generalized second laws at future null infinity, we show that additional terms appearing in the associated thermodynamic potentials admit a natural interpretation as work contributions. We demonstrate that certain non thermal vacuum states at null infinity allow for the operation of autonomous thermal engines and enable work extraction from the radiation. Extending the analysis to the Unruh vacuum in Schwarzschild and Kerr backgrounds, we obtain generalized grand potential type laws incorporating grey body effects and angular momentum fluxes. Altogether, our results clarify the thermodynamic description of black hole dynamics and place it within the broader framework of open quantum thermodynamics.

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arXiv2026

Quantum stochastic thermodynamics of macroscopic systems: an algebraic approach

We build a framework for the thermodynamics of macroscopic quantum systems. In contrast with approaches requiring access to the full density matrix, our framework relies on a coarse-grained description, based on measurement statistics of a few observables. When these observables commute, the outcomes define classical macrostates whose entropy is quantified by observational entropy, accounting for uncertainty about both the macrostate and the microstate within it. We extend this notion to non-commuting observables forming a subalgebra of the operator space, and use Jaynes' principle to define an algebra-dependent entropy interpolating between von Neumann and observational entropies. Given initial and final measurement sets, connected by internal and/or environment-induced dynamics, we derive a second law for the coarse-grained dynamics. Unlike formulations based on von Neumann entropy, our inequality captures irreversibility from both non-unitary environment-induced dynamics and internal equilibration. It takes the usual form of a positive entropy production when the system is initially at internal equilibrium, while correction terms capture nonequilibrium resources ignored by the coarse-graining. We also derive fluctuation theorems for coarse-grained thermodynamic quantities. Along a quasi-static path of measurement schemes, we identify quantum macroscopic notions of work and heat fulfilling the first and second laws, including an additional work contribution from manipulating the algebra to which the system is confined, through external constraints or quantum measurement backaction. Finally, we apply our framework to examples illustrating the impact of varying the coarse-graining scheme. Our approach unifies macroscopic and stochastic thermodynamics in a genuinely quantum framework, laying the basis for a versatile, experimentally friendly toolbox to analyze complex quantum dynamics.

quant-ph↗

arXiv2025

General covariance and boundary symmetry algebras

In general relativity as well as gauge theories, non-trivial symmetries can appear at boundaries. In the presence of radiation some of the symmetries are not Hamiltonian vector fields, hence the definition of charges for the symmetries becomes delicate. It can lead to the problem of field-dependent 2-cocycles in the charge algebra, as opposed to the central extensions allowed in standard classical mechanics. We show that if the Wald-Zoupas prescription is implemented, its covariance requirement guarantees that the algebra of Noether currents is free of field-dependent 2-cocycles, and its stationarity requirement further removes central extensions. Therefore the charge algebra admits at most a time-independent field-dependent 2-cocycle, whose existence depends on the boundary conditions. We report on new results for asymptotic symmetries at future null infinity that can be derived with this approach.

hep-th↗

arXiv2025

Spatially local energy density of gravitational waves

We propose a new set of BMS charges at null infinity, characterized by a super-translation flux that contains only the `hard' term. This is achieved with a specific corner improvement of the symplectic 2-form, and we spell the conditions under which it is unique. The charges are associated to a Wald-Zoupas symplectic potential, and satisfy all standard criteria: they are covariant, provide a center-less realization of the symmetry algebra, have vanishing flux in non-radiative spacetimes, and vanish in Minkowski. We use them to define a notion of spatially localized energy density of gravitational waves, and explain how it can be measured doing experiments which are purely local in space and over an extended period of time.

gr-qc↗

arXiv2024

Black hole thermodynamic potentials for asymptotic observers

The generalized second law states the total entropy of any closed system as the universe cannot decrease if we include black hole entropy. From the point of view of an asymptotic observer, a black hole can be described at late time as an open system at fixed temperature which can radiate energy and entropy to infinity. I argue that for massless free quantum fields propagating on a black hole background, we can define a black hole dynamical free energy using observables defined at future null infinity which decreases on successive cross sections. The proof of this spontaneous evolution law is similar to Wall's derivation of the generalized second law and relies on the monotonicity properties of the relative entropy. I discuss first the simpler case of the Schwarzschild background in which the grey body factor are neglected and show that in this case the free energy only depends on the Bondi mass, the Hawking temperature and the von Neumann entropy of the propagating quantum fields. Then I argue that taking into account the grey body factors adds a new term to the thermodynamic potential involving the number of particles detected at future null infinity conjugated to a chemical potential. Finally, I discuss the case of the Kerr black hole for which an angular momentum piece needs to be added to the free energy.

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arXiv2024

Center-less BMS charge algebra

We show that when the Wald-Zoupas prescription is implemented, the resulting charges realize the BMS symmetry algebra without any 2-cocycle nor central extension, at any cut of future null infinity. We refine the covariance prescription for application to the charge aspects, and introduce a new aspect for Geroch's super-momentum with better covariance properties. For the extended BMS symmetry with singular conformal Killing vectors we find that a Wald-Zoupas symplectic potential exists, if one is willing to modify the symplectic structure by a corner term. The resulting algebra of Noether currents between two arbitrary cuts is center-less. The charge algebra at a given cut has a residual field-dependent 2-cocycle, but time-independent and non-radiative. More precisely, super-rotation fluxes act covariantly, but super-rotation charges act covariantly only on global translations. The take home message is that in any situation where 2-cocycles appears in the literature, covariance has likely been lost in the charge prescription, and that the criterium of covariance is a powerful one to reduce ambiguities in the charges, and can be used also for ambiguities in the charge aspects.

hep-th↗

arXiv2023

General gravitational charges on null hypersurfaces

We perform a detailed study of the covariance properties of the symplectic potential of general relativity on a null hypersurface, and of the different polarizations that can be used to study conservative as well as leaky boundary conditions. This allows us to identify a one-parameter family of covariant symplectic potentials. We compute the charges and fluxes for the most general phase space with arbitrary variations. We study five symmetry groups that arise when different restrictions on the variations are included. Requiring stationarity as in the original Wald-Zoupas prescription selects a unique member of the family of symplectic potentials, the one of Chandrasekaran, Flanagan and Prabhu. The associated charges are all conserved on non-expanding horizons, but not on flat spacetime. We show that it is possible to require a weaker notion of stationarity which selects another symplectic potential, again in a unique way, and whose charges are conserved on both non-expanding horizons and flat light-cones. Furthermore, the flux of future-pointing diffeomorphisms at leading-order around an outgoing flat light-cone is positive and reproduces a tidal heating plus a memory term. We also study the conformal conservative boundary conditions suggested by the alternative polarization and identify under which conditions they define a non-ambiguous variational principle. Our results have applications for dynamical notions of entropy, and are useful to clarify the interplay between different boundary conditions, charge prescriptions, and symmetry groups that can be associated with a null boundary.

gr-qc↗

arXiv2023

Second law from the Noether current on null hypersurfaces

I study the balance law equation of surface charges in the presence of background fields. The construction allows a unified description of Noether's theorem for both global and local symmetries. From the balance law associated with some of these symmetries, I will discuss generalizations of Wald's Noether entropy formula and general entropy balance laws on null hypersurfaces based on the null energy conditions, interpreted as an entropy creation term. The entropy is generally the so-called improved Noether charge, a quantity that has recently been investigated by many authors, associated to null future-pointing diffeomorphisms. These local and dynamical definitions of entropy on the black hole horizon differ from the Bekenstein-Hawking entropy through terms proportional to the first derivative of the area along the null geodesics. Two different definitions of the dynamical entropy are identified, deduced from gravity symplectic potentials providing a suitable notion of gravitational flux which vanish on non-expanding horizons. The first one is proposed as a definition of the entropy for dynamical black holes by Wald and Zhang, and it satisfies the physical process first law locally. The second one vanishes on any cross section of Minkowski's light cone. I study general properties of its balance law. In particular, I look at first order perturbations around a non expanding horizon. Furthermore, I show that the dynamical entropy increases on the event horizon formed by a spherical symmetric collapse between the two stationary states of vanishing flux, i.e the initial flat light cone and the final stationary black hole. I compare this process to a phase transition, in which the symmetry group of the stationary black hole phase is enlarged by the supertranslations.

gr-qc↗

arXiv2023

A note on the physical process first law of black hole mechanics

I give a simple proof of the physical process first law of black hole thermodynamics including charged black holes, in which all perturbations are computed on the horizon.

gr-qc↗

arXiv2023

Wald-Zoupas prescription with (soft) anomalies

We show that the Wald-Zoupas prescription for gravitational charges is valid in the presence of anomalies and field-dependent diffeomorphism, but only if these are related to one another in a specific way. The geometric interpretation of the allowed anomalies is exposed looking at the example of BMS symmetries: They correspond to soft terms in the charges. We determine if the Wald-Zoupas prescription coincides with an improved Noether charge. The necessary condition is a certain differential equation, and when it is satisfied, the boundary Lagrangian of the resulting improved Noether charge contains in general a non-trivial corner term that can be identified a priori from a condition of anomaly-freeness. Our results explain why the Wald-Zoupas prescription works in spite of the anomalous behaviour of BMS transformations, and should be helpful to relate different branches of the literature on surface charges.

hep-th↗

arXiv2021

Black to white transition of a charged black hole

We present an exact solution of the Maxwell-Einstein equations, which describes the exterior of a charged spherical mass collapsing into its own trapping horizon and then bouncing back from an anti-trapping horizon at the same space location of the same asymptotic region. The solution is locally but not globally isometric to the maximally extended Reissner-Nordström metric and depends on seven parameters. It is regular, and defined everywhere except for a small region, where quantum tunnelling is expected. This region lies outside the mass: the mass-bounce and its near exterior are governed by classical general relativity. We discuss the relevance of this result for the fate of realistic black holes. We comment on possible effects of the classical instabilities and the Hawking radiation.

gr-qc↗

arXiv2021

Thermodynamics of light emission

Some interactions between classical or quantum fields and matter are known to be irreversible processes. Here we associate an entropy to the electromagnetic field from well-known notions of statistical quantum mechanics, in particular the notion of diagonal entropy. We base our work on the study of spontaneous emission and light diffusion. We obtain a quantity which allows to quantify irreversibility for a quantum and classical description of the electromagnetic field, that we can study and interpret from a thermodynamical point of view.

quant-ph↗

arXiv2020

Thermodynamics of precision in quantum nano-machines

Fluctuations strongly affect the dynamics and functionality of nanoscale thermal machines. Recent developments in stochastic thermodynamics have shown that fluctuations in many far-from-equilibrium systems are constrained by the rate of entropy production via so-called thermodynamic uncertainty relations. These relations imply that increasing the reliability or precision of an engine's power output comes at a greater thermodynamic cost. Here we study the thermodynamics of precision for small thermal machines in the quantum regime. In particular, we derive exact relations between the power, power fluctuations, and entropy production rate for several models of few-qubit engines (both autonomous and cyclic) that perform work on a quantised load. Depending on the context, we find that quantum coherence can either help or hinder where power fluctuations are concerned. We discuss design principles for reducing such fluctuations in quantum nano-machines, and propose an autonomous three-qubit engine whose power output for a given entropy production is more reliable than would be allowed by any classical Markovian model.

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