Related papers: Maximum R\'enyi Entropy Rate
Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is…
A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
We study the behaviour of R\'enyi entropies in a generic thermodynamic macrostate of an integrable model. In the standard quench action approach to quench dynamics, the R\'enyi entropies may be derived from the overlaps of the initial state…
The fundamental information-theoretic measures (the R\'enyi $R_{p}[\rho]$ and Tsallis $T_{p}[\rho]$ entropies, $p>0$) of the highly-excited (Rydberg) quantum states of the $D$-dimensional ($D>1$) hydrogenic systems, which include the…
We introduce a variant of the R\'enyi entropy definition that aligns it with the well-known H\"older mean: in the new formulation, the r-th order R\'enyi Entropy is the logarithm of the inverse of the r-th order H\"older mean. This brings…
We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and…
The analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the analyticity of these rates…
We study expected utility maximization problem with constant relative risk aversion utility function in a complete market under the reinforcement learning framework. To induce exploration, we introduce the Tsallis entropy regularizer, which…
We consider a singular control problem that aims to maximize the expected cumulative rewards, where the instantaneous returns depend on the state of a controlled process. The contributions of this paper are twofold. Firstly, to establish…
A principle of hierarchical entropy maximization is proposed for generalized superstatistical systems, which are characterized by the existence of three levels of dynamics. If a generalized superstatistical system comprises a set of…
We develop a nonequilibrium increment method in quantum Monte Carlo simulations to obtain the R\'enyi entanglement entropy of various quantum many-body systems with high efficiency and precision. To demonstrate its power, we show the…
We consider a robust asymptotic growth problem under model uncertainty in the presence of stochastic factors. We fix two inputs representing the instantaneous covariance for the asset price process $X$, which depends on an additional…
Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the…
Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum R\'enyi entropies. In order to do this, we appeal to a very general quantum encoding scheme that…
Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
We compute R\'enyi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two-dimensional quantum systems. The relative amount of uncertainty between two states depends on the uncertainty…