Related papers: Generalised entropy accumulation
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
Within its range of applicability, the Boltzmann equation seems unique in its capacity to accurately describe the transition from almost any initial state to a self-equilibrated thermal state. Using information-theoretic methods to rephrase…
We presented background information about various entropies in the literature. The pathway idea of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure and established connections to…
Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity $\beta$ can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and…
Quantum processes can exhibit scenarios beyond a fixed order of events. We propose information inequalities that, when violated, constitute sufficient conditions to certify quantum processes without a fixed causal order -- causally…
In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two…
We derive a universal inequality that provides a lower bound on the ensemble-averaged von Neumann entropy change in a quantum system subject to continuous measurement and dissipation. Our result clarifies how entropy production is…
In stochastic modeling, the excess entropy -- the mutual information shared between a process's past and future -- represents the fundamental lower bound of the memory needed to simulate its dynamics. However, this bound cannot be saturated…
We discuss the entropic criterion for separability of compound quantum systems for general non-additive entropic forms based on arbitrary concave functions $f$. For any separable state, the generalized entropy of the whole system is shown…
One of the most important aspects in any treatment of uncertain information is the rule of combination for updating the degrees of uncertainty. The theory of belief functions uses the Dempster rule to combine two belief functions defined by…
Complex systems that are characterized by strong correlations and fat-tailed distribution functions have been argued to be incompatible within the framework of Boltzmann-Gibbs entropy. As an alternative, so-called generalized entropies were…
For a broad class of input-output maps, arguments based on the coding theorem from algorithmic information theory (AIT) predict that simple (low Kolmogorov complexity) outputs are exponentially more likely to occur upon uniform random…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…
Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication or locomotion. Given time series observations of intra-, inter- or multicellular processes,…
PAE cannot be made a basis for either a generalized statistical mechanics or a generalized information theory. Either statistical independence must be waived, or the expression of the averaged conditional probability as the difference…
Quantum key distribution (QKD) achieves information-theoretic security, without relying on computational assumptions, by distributing quantum states. To establish secret bits, two honest parties exploit key distillation protocols over…
It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…