Related papers: Entropy method for the left tail

Simultaneous occurrences of extreme events need not imply symmetric or reciprocal tail dependence. However, most existing measures of extremal dependence are inherently symmetric and hence often fail to capture directional influence in tail…

The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…

Long-term training of large language models (LLMs) requires maintaining stable exploration to prevent the model from collapsing into sub-optimal behaviors. Entropy is crucial in this context, as it controls exploration and helps avoid…

Many major works in social science employ matching to make causal conclusions, but different matches on the same data may produce different treatment effect estimates, even when they achieve similar balance or minimize the same loss…

Recently, Zou obtained the generalized results on the bounds for Tsallis relative operator entropy. In this short paper, we give precise bounds for Tsallis relative operator entropy. We also give precise bounds of relative operator entropy.

We present several algorithms to generate tables for asymmetric numeral systems and prove that they are optimal in terms of discrepancy. In turn, this gives rise to the strongest proven bound on entropy loss. We further give improved…

Due to a lack of coherent analysis, many common practices of humankind preserve low-efficient procedures. Balancing tubes during centrifugation exemplifies such a problem in laboratory practice. Using combination of symmetry group theory…

We derive a bound for entropy production in terms of the mean of normalizable path-antisymmetric observables. The optimal observable for this bound is shown to be the signum of entropy production, which is often easier determined or…

Some preliminary evidence suggests the conjecture that the collective behaviour of systems having long-range interactions may be described more effectively by the Tsallis rather than by the Boltzmann/Gibbs/Shannon entropy. To this end, we…

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of $d$-dimensional bounded monotonic functions under $L^p$ norms. It is interesting to see that both the metric entropy and bracketing entropy…

Chang's lemma is a useful tool in additive combinatorics and the analysis of Boolean functions. Here we give an elementary proof using entropy. The constant we obtain is tight, and we give a slight improvement in the case where the…

Living systems maintain or increase local order by working against the Second Law of Thermodynamics. Thermodynamic consistency is restored as they dissipate heat, thereby increasing the net entropy of their environment. Recently introduced…

This note is devoted to the study of the maximum of the excursion of a random walk with negative drift and light-tailed increments. More precisely, we determine the local asymptotics of the joint distribution of the length, maximum and the…

There is a conception that Boltzmann-Gibbs statistics cannot yield the long tail distribution. This is the justification for the intensive research of nonextensive entropies (i.e. Tsallis entropy and others). Here the error that caused this…

Chernoff's bound binds a tail probability (ie. $Pr(X \ge a)$, where $a \ge EX$). Assuming that the distribution of $X$ is $Q$, the logarithm of the bound is known to be equal to the value of relative entropy (or minus Kullback-Leibler…

We review recent progress in understanding certain aspects of the thermodynamics of black holes and other horizons. Our discussion centers on various ``entropy bounds'' which have been proposed in the literature and on the current…

We analyze phase transitions in the conditional entropy of a sequence caused by a change in the conditional variables. Such transitions happen, for example, when training to learn the parameters of a system, since the transition from the…

Calculation of topological order parameters, such as the topological entropy and topological mutual information, are used to determine whether states possess topological order. Their calculation is expected to give reliable results when the…

An efficient approach to the calculation of the $\epsilon$-entropy is proposed. The method is based on the idea of looking at the information content of a string of data, by analyzing the signal only at the instants when the fluctuations…

We study the validity of Bekenstein's entropy bound for a charged black hole in the context of nonlinear electrodynamics. Bekenstein's inequalities are commonly understood as universal relations between the entropy, the charge, the…