ABSTRACT We reconsider the quantum energetics and quantum thermodynamics of the charging process of a simple, two‐component quantum battery model made up of a charger qubit and a single–cell battery qubit. We allow for the initial quantum state of the charger to lie anywhere on the surface of the Bloch sphere, and find the generalized analytical expressions describing the stored energy, ergotropy, and capacity of the battery, all of which depend upon the initial Bloch sphere polar angle in a manner evocative of the quantum area theorem. The origin of the ergotropy produced, as well as the genesis of the battery capacity, can be readily traced back to the quantum coherences and population inversions generated (and the balance between these two mechanisms is contingent upon the starting Bloch polar angle). Importantly, the ergotropic charging power and its associated optimal charging time display notable deviations from standard results, which disregard thermodynamic considerations. Our theoretical groundwork may be useful for guiding forthcoming experiments in quantum energy science based upon coupled two‐level systems.

Verification of the black hole area law with GW230814.

Abstract We evaluate the validity of the generalized second law for Kerr black holes perturbed by fermionic and bosonic fields. We derive that the critical frequency for a test field below which the area of a Kerr black hole would decrease, coincides with the superradiance limit which pertains to bosonic fields. The fact that the absorption of fermionic fields with arbitrarily low frequencies is allowed, leads to a generic violation of the generalized second law as both the black hole and the environment lose entropy. The result does not contradict the proof of the area theorem which pre-assumes the validity of the null energy condition. We also construct a thought experiment involving bosonic fields to check whether the minimum increase in the area can compensate for the decrease in the entropy of the environment. We minimize the entropy increase by considering a black hole at the extremal limit, perturbed by a bosonic field at the superradiance limit. We show that the generalized second law remains valid for bosonic fields that satisfy the null energy condition. The result does not require the employment of entropy bounds when one assigns von Neumann entropy to test fields.

Abstract The goal of the present work is to study optimal transport on null hypersurfaces inside Lorentzian manifolds. The challenge here is that optimal transport along a null hypersurface is completely degenerate, as the cost takes only the two values 0 and $$+\infty $$ + ∞ . The tools developed in the manuscript enable to give an optimal transport characterization of the null energy condition (namely, non-negative Ricci curvature in the null directions) for Lorentzian manifolds in terms of convexity properties of the Boltzmann–Shannon entropy along null-geodesics of probability measures. We obtain as applications: a stability result under convergence of spacetimes, a comparison result for null-cones, and the Hawking area theorem (both in sharp form, for possibly weighted measures, and with apparently new rigidity statements).

We extend the area theorem toward the analytical description of the coherent pulse propagation in a quantum-dot (QD) laser medium in a ring-cavity setup. We apply the derived area theorem to demonstrate the appearance of the stable coherent mode-locking regime in a single-section ring-cavity QD laser. The paper findings showcase the possibility of making compact solid-state sources of ultrashort pulses with pulse duration well beyond the gain bandwidth limit.

The active use of resonators in quantum technologies increases the interest of their application in the creation of optical and microwave quantum memory. The use of photon and spin echoes opens up the possibility of storing a large number of light pulses in one such memory cell. High efficiency of such quantum memory is achieved in an optically dense resonant media, in which the formation of a photon (spin) echo can be accompanied by an increase in the nonlinear interaction of light with atoms causing the appearance of multiple echo signals. In this paper, we develop the pulse area approach to study general nonlinear properties of the primary and multi-pulse echo signals excited in a two-level atomic ensemble located in ring cavities with volumetric and surface modes. Conditions under which one or more echo pulses can be generated are analyzed. The solutions obtained are compared with recent experimental results. We show that the area theorem is one of the simplest and most powerful analytical tools for studying a highly nonlinear and dynamical process of the formation of the sequence of photon/spin echo signals in resonant media inside the resonator.

By introducing significant anomalous dispersion in a fiber laser, we numerically obtained a mode-locked pulse with a pulse duration of 1.9 ns and 3-dB bandwidth of 1.3 pm, which corresponds to a time-bandwidth product of about 0.317. The output pulse energy is 1.9 nJ. The variation of output pulses versus introduced dispersion is presented. It is found that, determined by the soliton area theorem, transform-limited nanosecond mode-locked pulses could be expected. In addition, we numerically observed the period doubling phenomenon by increasing the pump power, which indicates that fiber lasers operating in the regime of significant anomalous dispersion can still exhibit rich nonlinear dynamics based on nanosecond pulses. For a fixed cavity dispersion, the pulse energy achievable is limited by the appearance of pulse nonlinear dynamics.

The notion of Hankel determinant Hq in univalent functions theory is initiated by Noonan and Thomas while studying it for areally mean multivalent mappings. This determinant has significant role while dealing with singularities and particularly it’s important for analyzing integral coefficient. Fekete-Szeg¨o functional used in the study of the area theorem is a particular case of this determinant. We explore a known class of holomorphic mappings which is related with the various classes of functions with conjugate symmetric points We also study upper bounds in different settings of the coefficients of these mappings. We also relate our exploration with the existing literature of the subject.

In this paper, we introduce some new families of analytic functions by using Hadamard product while keeping conic like domains in view. Like the area theorem, we determine sufficient conditions as well as characterizations of these functions. Furthermore, we develop a connection between Poisson distribution series whose coefficients are probabilities of some events occurring in a fixed duration of time or space under certain conditions and some subclasses of analytic functions. To be more precise, we investigate such connections with the classes of analytic functions with complex as well as non-negative coefficients by determining sufficient conditions along with characterizations of functions involving Poisson distribution and its related variants.

We consider a time-dependent O1/G deformation of pure de Sitter (dS) space in dS gravity coupled to a massless scalar field. It is the dS counterpart of the AdS Janus deformation and interpolates two asymptotically dS spaces in the far past and the far future with a single deformation parameter. The Penrose diagram can be elongated along the time direction indefinitely as the deformation becomes large. After studying the classical properties of the geometry such as the area theorem and the fluctuation by a matter field, we explore the algebraic structure of the field operators on the deformed spacetime. We argue that the algebra is a von Neumann factor of type II∞ for small deformations, but there occurs a transition to type I∞ as the deformation increases so that the neck region of the deformed space becomes a Lorentzian cylinder.

Hawking’s black hole area theorem provides a geometric realization of the second law of thermodynamics and constrains gravitational processes. In this work we explore a one-parameter extension of this constraint formulated in terms of the monotonicity properties of Rényi entropies. We focus on black hole mergers in asymptotically AdS space and determine new restrictions which these Rényi second laws impose on the final state. We evaluate the entropic inequalities starting from the thermodynamic ensembles description of black hole geometries, and find that for many situations they set more stringent bounds than those imposed by the area increase theorem.

We show how the area theorem is applicable to the analytical description of the nonlinear interaction of surface plasmon modes with resonant two-level atoms. A closed analytical solution is obtained, which shows that surface plasmons can form long-propagating 2π pulses when interacting with an optically dense two-level atomic ensemble. The possible applications of the surface pulse area theorem and the conditions for the detection of 2π surface plasmon pulses are discussed.

Sky marginalization in black hole spectroscopy and tests of the area theorem

Let Σ H k ( p ) \Sigma _H^k(p) be the class of sense-preserving univalent harmonic mappings defined on the open unit disk D \mathbb {D} of the complex plane with a simple pole at z = p ∈ ( 0 , 1 ) z=p \in (0,1) that have k k -quasiconformal extensions ( 0 ≤ k > 1 0\leq k>1 ) onto the extended complex plane. In this article, we obtain an area theorem for this class of functions.

Hawking’s black hole area theorem was proven using the null energy condition (NEC), a pointwise condition violated by quantum fields. The violation of the NEC is usually cited as the reason that black hole evaporation is allowed in the context of semiclassical gravity. Here we provide two generalizations of the classical black hole area theorem: first, a proof of the original theorem with an averaged condition, the weakest possible energy condition to prove the theorem using focusing of null geodesics. Second, a proof of an area-type result that allows for the shrinking of the black hole horizon but provides a bound on it. This bound can be translated to a bound on the black hole evaporation rate using a condition inspired from quantum energy inequalities. Finally, we show how our bound can be applied to two cases that violate classical energy conditions.

We present a semi-rigorous justification of Bekenstein's Generalized Second Law of Thermodynamics applicable to a universe with black holes present, based on a generic quantum gravity formulation of a black hole spacetime, where the bulk Hamiltonian constraint plays a central role. Specializing to Loop Quantum Gravity, and considering the inspiral and post-ringdown stages of binary black hole merger into a remnant black hole, we show that the Generalized Second Law implies a lower bound on the non-perturbative LQG correction to the Bekenstein-Hawking area law for black hole entropy. This lower bound itself is expressed as a function of the Bekenstein-Hawking area formula for entropy. Results of the analyses of LIGO-VIRGO-KAGRA data recently performed to verify the Hawking Area Theorem for binary black hole merger are shown to be entirely consistent with this Loop Quantum Gravity-induced inequality. However, the consistency is independent of the magnitude of the LQG corrections to black hole entropy, depending only on the negative algebraic sign of the quantum correction. We argue that results of alternative quantum gravity computations of quantum black hole entropy, where the quantum entropy exceeds the Bekenstein-Hawking value, may not share this consistency.

Motivated by the known mathematical and physical problems arising from the current mathematical formalization of the physical spatio-temporal continuum, as a substantial technical clarification of our earlier attempt (Etesi in Found Sci 25:327–340, 2020), the aim in this paper is twofold. Firstly, by interpreting Chaitin’s variant of Gödel’s first incompleteness theorem as an inherent uncertainty or fuzziness present in the set of real numbers, a set-theoretic entropy is assigned to it using the Kullback–Leibler relative entropy of a pair of Riemannian manifolds. Then exploiting the non-negativity of this relative entropy an abstract Hawking-like area theorem is derived. Secondly, by analyzing Noether’s theorem on symmetries and conserved quantities, we argue that whenever the four dimensional space-time continuum containing a single, stationary, asymptotically flat black hole is modeled by the set of real numbers in the mathematical formulation of general relativity, the hidden set-theoretic entropy of this latter structure reveals itself as the entropy of the black hole (proportional to the area of its “instantaneous” event horizon), indicating that this apparently physical quantity might have a pure set-theoretic origin, too.

Area theorem in a ring laser cavity

We investigate the feasibility of minimum absorption and minimum broadening of pulse propagation in an inhomogeneously broadened semiconductor quantum dot medium. The phonon interaction is inevitable in studying any semiconductor quantum dot system. We have used the polaron transformation technique to deal with quantum dot phonon interaction in solving system dynamics. We demonstrate that a short pulse can propagate inside the medium with minimal absorption and broadening in pulse shape. The stable pulse area becomes slightly higher than the prediction of the pulse area theorem and is also dependent on the environment temperature. The change in the final pulse shape is explained very well by numerically solving the propagation equation supported by the susceptibility of the medium. Our system also exhibits the pulse breakup phenomena for higher input pulse areas. Therefore, the considered scheme can have important applications in quantum communication, quantum information, and mode-locking with the advantage of scalability and controllability.

ABSTRACT Hawking’s area theorem is one of the fundamental laws of black holes (BHs), which has been tested at a confidence level of $\sim 95~{{\ \rm per\ cent}}$ with gravitational wave (GW) observations by analysing the inspiral and ringdown portions of GW signals, independently. In this work, we propose to carry out the test in a new way with the hierarchical triple merger (i.e. two successive BH mergers occurred sequentially within the observation window of GW detectors), for which the properties of the progenitor BHs and the remnant BH of the first coalescence can be inferred from the inspiral portions of the two mergers. As revealed in our simulations, the BH area law can be well confirmed for some plausible hierarchical triple merger events detectable in LIGO/Virgo/KAGRA/LIGO-India’s O4/O5 runs. Our proposed method provides significant facilitation for testing the area law and complements previous methods.