For timed languages, we define size measures: volume for languages with a fixed finite number of events, and entropy (growth rate) as asymptotic measure for an unbounded number of events. These measures can be used for quantitative comparison of languages, and the entropy can be viewed as information contents of a timed language. For languages accepted by deterministic timed automata, we give e...

Ill-posed inverse problems of the form y = Xp where y is J-dimensional vector of a data, p is m-dimensional probability vector which can not be measured directly and matrix X of observable variables is a known J ×m matrix, J < m, are frequently solved by Shannon’s entropy maximization (MaxEnt, ME). Several axiomatizations were proposed (see for instance [1], [2], [3], [4], [5], [6], [7], [8], a...

We extend the definition of nonadiabatic entropy production given for Markovian systems by Esposito and Van den Broeck [Phys. Rev. Lett. 104, 090601 (2010)], to arbitrary non-Markov ergodic dynamics. We also introduce a notion of stability characterizing non-Markovianity. For stable non-Markovian systems, the nonadiabatic entropy production satisfies an integral fluctuation theorem, leading to ...

We set out to demonstrate that the Rényi entropies with parameter α are better thought of as operating in a type of non-linear semiring called a positive semifield. We show how the Rényi’s postulates lead to Pap’s g-calculus where the functions carrying out the domain transformation are Renyi’s information function and its inverse. In its turn, Pap’s g-calculus under Rényi’s information functio...

In earlier work we presented a foundation for the Second Law of Classical Thermodynamics in terms of the Entropy Principle. More precisely, we provided an empirically accessible axiomatic derivation of an entropy function defined on all equilibrium states of all systems that has the appropriate additivity and scaling properties and whose increase is a necessary and sufficient condition for an a...

In earlier work, we presented a foundation for the second law of classical thermodynamics in terms of the entropy principle. More precisely, we provided an empirically accessible axiomatic derivation of an entropy function defined on all equilibrium states of all systems that has the appropriate additivity and scaling properties, and whose increase is a necessary and sufficient condition for an...

Precisely describing the formation and evolution rules of coal-rock fracturing crack have great value on reservoir fracturing improvement and highly efficient mining of coal bed methane well. In this paper, a non-linear dynamic method is used to study crack damage evolution behavior of coal-rock fracturing. Considering distribution characteristics of natural cracks in coal-rock, and based on da...

We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians. Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian ...

We calculate the quantum corrections to the entropy of a very large black hole, coming from the theory of a D-dimensional, non-critical bosonic string. We show that, for D > 2, as a result of modular invariance the entropy is ultraviolet finite, although it diverges in the infrared (while for D = 2 the entropy contains both ultraviolet and infrared divergences). The issue of modular invariance ...

This document describes a package of Python code for implementing various non-parametric continuous entropy estimators (and some discrete ones for convenience). After describing installation, Sec. 4 provides a wide-ranging discussion of technical, theoretical, and numerical issues surrounding entropy estimation. Sec. 5 provides references to the relevant literature for each estimator implemente...