Asymptotic Entropy Research Articles

Off-policy asymptotic and adaptive maximum entropy deep reinforcement learning

Off-policy asymptotic and adaptive maximum entropy deep reinforcement learning

Stochastic pairwise preference convergence in Bayesian agents.

Beliefs inform the behavior of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to explain how preferences evolve in cases of simple agent interactions. In this paper, we derive a Gaussian, pairwise agent interaction model to study how preferences converge when driven by observation of each other's behaviors. We show that the dynamics of convergence resemble an Ornstein-Uhlenbeck process, a common model in nonequilibrium stochastic dynamics. Using standard analytical and computational techniques, we find that the hyperprior magnitudes, representing the learning time, determine the convergence value and the asymptotic entropy of the preferences across pairs of agents. We also show that the dynamical variance in preferences is characterized by a relaxation time t^{★} and compute its asymptotic upper bound. This formulation enhances the existing toolkit for modeling stochastic, interactive agents by formalizing leading theories in learning theory, and builds towards more comprehensive models of open problems in principal-agent and market theory.

Conditioning in Tropical Probability Theory.

We define a natural operation of conditioning of tropical diagrams of probability spaces and show that it is Lipschitz continuous with respect to the asymptotic entropy distance.

Quantum flux operators for Carrollian diffeomorphism in general dimensions

We construct Carrollian scalar field theories in general dimensions, mainly focusing on the boundaries of Minkowski and Rindler spacetime, whose quantum flux operators form a faithful representation of Carrollian diffeomorphism up to a central charge, respectively. At future/past null infinity, the fluxes are physically observable and encode rich information of the radiation. The central charge may be regularized to be finite by the spectral zeta function or heat kernel method on the unit sphere. For the theory at the Rindler horizon, the effective central charge is proportional to the area of the bifurcation surface after regularization. Moreover, the zero mode of supertranslation is identified as the modular Hamiltonian, linking Carrollian diffeomorphism to quantum information theory. Our results may hold for general null hypersurfaces and provide new insight in the study of the Carrollian field theory, asymptotic symmetry group and entanglement entropy.

Entanglement dynamics with string measurement operators

We explain how to apply a Gaussian-preserving operator to a fermionic Gaussian state. We use this method to study the evolution of the entanglement entropy of an Ising spin chain undergoing a quantum-jump dynamics with string measurement operators. We find that, for finite-range string operators, the asymptotic entanglement entropy exhibits a crossover from a logarithmic to an area-law scaling with the system size, depending on the Hamiltonian parameters as well as on the measurement strength. For ranges of the string which scale extensively with the system size, the asymptotic entanglement entropy shows a volume-law scaling, independently of the measurement strength and the Hamiltonian dynamics. The same behavior is observed for the measurement-only dynamics, suggesting that measurements may play a leading role in this context.

Thermal entropy in Calabi-Yau quantum mechanics

We consider the von Neumann entropy of a thermal mixed state in quantum systems derived from mirror curves, where the kinetic terms are exponential functions of the momentum operators. Using the mathematical results on the asymptotics of the energy eigenvalues, we compute the asymptotic entropy in high temperature limit and compare with that of the conventional models. We discuss the connections with some folklores in quantum gravity, particularly on the finiteness of entropy.

Two-parameter family of distributions: Properties, estimation, and applications

In this paper, a new flexible two-parameter family of distributions is introduced. Some mathematical properties, such as asymptotic behavior, moments, stochastic order, entropy, and quantile function, are examined. A special case of this family is introduced called Gemeay–Zeghdoudi distribution. The unknown parameters of the Gemeay–Zeghdoudi distribution are estimated via many estimators. The efficiency of the estimators is compared with a Monte Carlo simulation. The applicability of the new distribution is illustrated by the annual maximum flood and survival times of patients with breast cancer real data analyses.

Entropy of black holes coupled to a scalar field

The Hamiltonian approach to black hole entropy, recently proposed in the framework of Poincar\'e gauge theory, is extended by including the scalar matter. The improved approach is used to analyse asymptotic charges and entropy of a typical black hole with scalar hair in two complementary dynamical settings, in GR and in the teleparallel gravity. In both cases, the results confirm the validity of the first law.

On Enumeration and Entropy of Ribbon Tilings

The paper considers ribbon tilings of large regions and their per-tile entropy (the logarithm of the number of tilings divided by the number of tiles). For tilings of general regions by tiles of length $n$, we give an upper bound on the per-tile entropy as $n - 1$. For growing rectangular regions, we prove the existence of the asymptotic per tile entropy and show that it is bounded from below by $\log_2 (n/e)$ and from above by $\log_2(en)$. For growing generalized "Aztec Diamond" regions and for growing "stair" regions, the asymptotic per-tile entropy is calculated exactly as $1/2$ and $\log_2(n + 1) - 1$, respectively.

Non-Holomorphic Cycles and Non-BPS Black Branes

We study extremal non-BPS black holes and strings arising in M-theory compactifications on Calabi–Yau threefolds, obtained by wrapping M2 branes on non-holomorphic 2-cycles and M5 branes on non-holomorphic 4-cycles. Using the attractor mechanism we compute the black hole mass and black string tension, leading to a conjectural formula for the asymptotic volumes of connected, locally volume-minimizing representatives of non-holomorphic, even-dimensional homology classes in the threefold, without knowledge of an explicit metric. In the case of divisors we find examples where the volume of the representative corresponding to the black string is less than the volume of the minimal piecewise-holomorphic representative, predicting recombination for those homology classes and leading to stable, non-BPS strings. We also compute the central charges of non-BPS strings in F-theory via a near-horizon $$AdS_3$$ limit in 6d which, upon compactification on a circle, account for the asymptotic entropy of extremal non-supersymmetric 5d black holes (i.e., the asymptotic count of non-holomorphic minimal 2-cycles).

Entropy of Kerr-Newman-AdS black holes with torsion

The canonical approach to black hole entropy in Poincar\'e gauge theory without matter is extended to include the Maxwell field as a matter source. The new formalism is used to calculate asymptotic charges and entropy of Kerr-Newmann-AdS black holes with torsion. The result implies that the first law, with a nontrivial contribution of the Maxwell field, takes the same form as in general relativity.

Entropy estimation in bidimensional sequences.

We investigate the performance of entropy estimation methods, based either on block entropies or compression approaches, in the case of bidimensional sequences. We introduce a validation data set made of images produced by a large number of different natural systems, in the vast majority characterized by long-range correlations, which produce a large spectrum of entropies. Results show that the framework based on lossless compressors applied to the one-dimensional projection of the considered data set leads to poor estimates. This is because higher dimensional correlations are lost in the projection operation. The adoption of compression methods which do not introduce dimensionality reduction improves the performance of this approach. By far, the best estimation of the asymptotic entropy is generated by the faster convergence of the traditional block-entropies method. As a by-product of our analysis, we show how a specific compressor method can be used as a potentially interesting technique for automatic detection of symmetries in textures and images.

Measuring postquench entanglement entropy through density correlations

Following a sudden change of interactions in an integrable system of one-dimensional fermions, we analyze the dependence of the static structure factor on the observation time after the quantum quench. At small waiting times after the quench, we map the system to noninteracting bosons such that we are able to extract their occupation numbers from the Fourier transform of the density-density correlation function, and use these to compute a bosonic entropy from a diagonal ensemble. By comparing this bosonic entropy with the asymptotic steady-state entanglement entropy per fermion computed with exact diagonalization, we find excellent agreement.Received 8 December 2021Revised 17 March 2022Accepted 22 March 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L022023Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBosonizationCharge density wavesEntanglement entropyQuantum quenchTechniquesExact diagonalizationLuttinger liquid modelCondensed Matter, Materials & Applied PhysicsQuantum InformationStatistical Physics

Holographic deconfined QGP phase diagram and entropy with an anomalous flow in a magnetic field background

We assume that the initial hydrodynamic environment is a quark gluon plasma (QGP) phase where merely $u$ and $d$ quarks are considered when adding a magnetic field. When considering the chiral magnetic effect in relativistic heavy ion collisions, an anomalous current will be formed in the QGP environment. The chiral magnetic current formed by these $u$ and $d$ quarks has an impact on the heavy quarkonium. By using fluid/gravity duality, the metric with anomalous flow is established by using fluid/gravity duality, so as to introduce the magnetic field effect into the corresponding metric. And then we use heavy quarkonium as a probe to study phase transition, and utilize the effective string tension of the heavy quarkonium to study phase transition by AdS/QCD theory. The characteristics of reporting inverse magnetic catalysis for the confinement-deconfinement transition with anomalous flow are in qualitative agreement with lattice QCD findings. The heavy-quarkonium asymptotic entropy distributions with different magnetic field around the confinement-deconfinement transition temperature are given in the paper.

Fluctuation and entropy in spectrally constrained random fields

We investigate the statistical properties of translation invariant random fields (including point processes) on Euclidean spaces (or lattices) under constraints on their spectrum or structure function. An important class of models that motivate our study are hyperuniform and stealthy hyperuniform systems, which are characterised by the vanishing of the structure function at the origin (resp., vanishing in a neighbourhood of the origin). We show that many key features of two classical statistical mechanical measures of randomness - namely, fluctuations and entropy, are governed only by some particular local aspects of their structure function. We obtain exponents for the fluctuations of the local mass in domains of growing size, and show that spatial geometric considerations play an important role - both the shape of the domain and the mode of spectral decay. In doing so, we unveil intriguing oscillatory behaviour of spatial correlations of local masses in adjacent box domains. We describe very general conditions under which we show that the field of local masses exhibit Gaussian asymptotics, with an explicitly described limit. We further demonstrate that stealthy hyperuniform systems with joint densities exhibit degeneracy in their asymptotic entropy per site. In fact, our analysis shows that entropic degeneracy sets in under much milder conditions than stealthiness, as soon as the structure function fails to be logarithmically integrable.

The properties of entropy as a measure of randomness in a clinical trial

We study entropy as a measure of randomness in a sequential clinical trial. For any randomization design, we consider the well-known sequence of conditional treatment assignment probabilities, Pn, which complements the random allocation proportion. We then use Pn to formulate and prove a statement about conditions for the asymptotic mean entropy of a randomization design to achieve its optimum value. We compare both response-adaptive and non response adaptive randomization designs with respect to the asymptotic mean entropy, connecting the variance of Pn to the asymptotic mean entropy under normality. Then we explore whether both Pn, as well as the allocation proportion, may have zero asymptotic variance.

Thermodynamics of Riemannian Kerr-AdS black holes in Poincaré gauge theory

A Hamiltonian approach to black hole entropy is used to study Riemannian Kerr-AdS solutions in the general, parity-violating Poincaré gauge theory. Asymptotic charges and entropy are entirely determined by the parity-even sector of the theory, since the related parity-odd contributions vanish. The resulting thermodynamic variables are shown to satisfy the first law of black hole thermodynamics.

Thermodynamics of Kerr-AdS black holes in general Poincaré gauge theory

A Hamiltonian variational approach is used to study asymptotic charges and entropy of Kerr--anti--de Sitter black holes in the general Poincar\'e gauge theory, with both even and odd parity modes. The results turn out to be the same as those found earlier in the sector of parity invariant Lagrangians.

Entropy-Based Classification of Elementary Cellular Automata under Asynchronous Updating: An Experimental Study.

Classification of asynchronous elementary cellular automata (AECAs) was explored in the first place by Fates et al. (Complex Systems, 2004) who employed the asymptotic density of cells as a key metric to measure their robustness to stochastic transitions. Unfortunately, the asymptotic density seems unable to distinguish the robustnesses of all AECAs. In this paper, we put forward a method that goes one step further via adopting a metric entropy (Martin, Complex Systems, 2000), with the aim of measuring the asymptotic mean entropy of local pattern distribution in the cell space of any AECA. Numerical experiments demonstrate that such an entropy-based measure can actually facilitate a complete classification of the robustnesses of all AECA models, even when all local patterns are restricted to length 1. To gain more insights into the complexity concerning the forward evolution of all AECAs, we consider another entropy defined in the form of Kolmogorov–Sinai entropy and conduct preliminary experiments on classifying their uncertainties measured in terms of the proposed entropy. The results reveal that AECAs with low uncertainty tend to converge remarkably faster than models with high uncertainty.

Asymptotic entropy of the Gibbs state of complex networks

In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state for a few classes of graphs and studied their behavior with changing graph order and temperature. We illustrate our analytical results with numerical simulations for Erdős–Rényi, Watts–Strogatz, Barabási–Albert and Chung–Lu graph models and a few real-world graphs. Our results show that the behavior of Gibbs entropy as a function of the temperature differs for a choice of real networks when compared to the random Erdős–Rényi graphs.