Supplementary Material: Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection Gabriel Martos 1, ̊, Nicolás Hernández 2, Alberto Muñoz 2 and Javier M. Moguerza 3 1 Universidad de Buenos Aires and CONICET; [email protected] 2 Universidad Carlos III de Madrid; {nihernan,albmun}@est-econ.uc3m.es 3 Universidad Rey Juan Carlos; [email protected] ...

1. The Physics of Information 2 2. Thermodynamics 4 2.1. The laws 5 2.2. Free energy 8 3. Statistical mechanics 9 3.1. Definitions and postulates 10 3.2. Counting microstates for a system of magnetic spins 11 3.3. The Maxwell-Boltzmann-Gibbs distribution 12 3.4. Free energy revisited 13 3.5. Gibbs entropy 13 4. Nonlinear dynamics 15 4.1. The ergodic hypothesis 16 4.2. Chaos and limits to predic...

A new definition of t-entropy for transfer operators The article presents a new definition of t-entropy that makes it more explicit and simplifies the process of its calculation. In the series of articles [1, 2, 3, 4, 5, 6] there have been established the variational principles for the spectral radii of weighted shift and transfer operators generated by an arbitrary dynamical system. These prin...

We extend the results of Walters on the uniqueness of invariant measures with maximal entropy on compact groups to an arbitrary locally compact group. We show that the maximal entropy is attained at the left Haar measure and the measure of maximal entropy is unique.

Heart Rate Variability (HRV) is defined as the variations between consecutive instantaneous heart rates that occur in the heart as a consequence of a complex internal dynamic balance. Nonlinear analysis of HRV is helpful to assess the cardiac health noninvasively. Approximate Entropy and Sample Entropy are mathematical algorithms to measure the predictability or repeatability with in a time ser...

in this work, one and two-dimensional lattices are studied theoretically by a statistical mechanical approach. the nearest and next-nearest neighbor interactions are both taken into account, and the approximate thermodynamic properties of the lattices are calculated. the results of our calculations show that: (1) even though the next-nearest neighbor interaction may have an insignificant effect...

In this paper, a new invariant called {it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {it conditional logical entropy} is defined and then some of its properties are studied.  The invariance of the {it logic entropy} of a system  under isomorphism is proved. At the end,  the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolm...

Recently, we derived an improved universal upper bound to the entropy of a charged system S ≤ π(2Eb − q 2)/¯ h. There was, however, some uncertainty in the value of the numerical factor which multiplies the q 2 term. In this paper we remove this uncertainty; we rederive this upper bound from an application of the generalized second law of thermodynamics to a gedanken experiment in which an entr...

By replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo average (KN-averages) or quasilinear mean and further imposing the additivity constraint, Rényi proposed the first formal generalization of Shannon entropy. Using this recipe of Rényi, one can prepare only two information measures: Shannon and Rényi entropy. Indeed, using this formalism Rényi characterized these additive en...

Long memory or long range dependency is an important phenomenon that may arise in the analysis of time series or spatial data. Most of the definitions of long memory of a stationary process X = {X1, X2, · · · , } are based on the second-order properties of the process. The excess entropy of a stationary process is the summation of redundancies which relates to the rate of convergence of the con...