scholarly journals Consistency of the plug-in estimator of the entropy rate for ergodic processes

2016 ◽  
Author(s):  
Lukasz Debowski
Keyword(s):  
Entropy Rate ◽  
Ergodic Processes

About definition of the local entropy rate of production in experiment of pulse electric heating

2020 ◽  
pp. 29-34
Author(s):  
Alexandr V. Kostanovskiy ◽  
Margarita E. Kostanovskaya
Keyword(s):  
Thermal Diffusivity ◽  
Electric Heating ◽  
Thermal Capacity ◽  
Entropy Rate ◽  
Initial Time ◽  
Local Entropy ◽  
Linear Mode ◽  
Electric Capacity ◽  
Definition Of ◽  
Pulse Electric

Work is devoted to studying of a linear mode thermodynamic – a mode which is actively investigated now. One of the main concepts of a linear mode – local entropy rate of production. The purpose of given article consists in expansion of a circle of problems for which it is possible to calculate a local entropy rate of production, namely its definition, using the experimental “time-temperature” curves of heating/cooling. “Time-temperature” curves heating or cooling are widely used in non-stationary thermophysical experiments at studying properties of substances and materials: phase transitions of the first and second sort, a thermal capacity, thermal diffusivity. The quantitative substantiation of the formula for calculation of the local entropy rate of production in which it is used thermogram (change of temperature from time) which is received by a method of pulse electric heating is resulted. Initial time dependences of electric capacity and temperature are measured on the sample of niobium in a microsecond range simultaneously. Conformity of two dependences of the local entropy rate of production from time is shown: one is calculated under the known formula in which the brought electric capacity is used; another is calculated, using the thermogram.

scholarly journals Lumpings of Markov Chains, Entropy Rate Preservation, and Higher-Order Lumpability

2014 ◽  
Vol 51 (4) ◽  
pp. 1114-1132 ◽  
Author(s):  
Bernhard C. Geiger ◽  
Christoph Temmel
Keyword(s):  
Growth Rate ◽  
Markov Chain ◽  
Sufficient Conditions ◽  
Entropy Rate ◽  
Transition Graph ◽  
Order Markov Chain ◽  
Finite State ◽  
Random Growth ◽  
Irreducible Markov Chain ◽  
Finite State Space

A lumping of a Markov chain is a coordinatewise projection of the chain. We characterise the entropy rate preservation of a lumping of an aperiodic and irreducible Markov chain on a finite state space by the random growth rate of the cardinality of the realisable preimage of a finite-length trajectory of the lumped chain and by the information needed to reconstruct original trajectories from their lumped images. Both are purely combinatorial criteria, depending only on the transition graph of the Markov chain and the lumping function. A lumping is strongly k-lumpable, if and only if the lumped process is a kth-order Markov chain for each starting distribution of the original Markov chain. We characterise strong k-lumpability via tightness of stationary entropic bounds. In the sparse setting, we give sufficient conditions on the lumping to both preserve the entropy rate and be strongly k-lumpable.

scholarly journals Variation in the input: a case study of manner class frequencies

2012 ◽  
Vol 40 (5) ◽  
pp. 1091-1122 ◽  
Author(s):  
ROBERT DALAND
Keyword(s):  
Frequency Variation ◽  
Natural Background ◽  
Frequency Distributions ◽  
Language Varieties ◽  
Ergodic Processes ◽  
Language Variety ◽  
Sources Of Variation ◽  
Manner Of Articulation ◽  
Discourse Topic

ABSTRACTWhat are the sources of variation in the input, and how much do they matter for language acquisition? This study examines frequency variation in manner-of-articulation classes in child and adult input. The null hypothesis is that segmental frequency distributions of language varieties are unigram (modelable by stationary, ergodic processes), and that languages are unitary (modelable as a single language variety). Experiment I showed that English segments are not unigram; they exhibit a ‘bursty’ distribution in which the local frequency varies more than expected by chance alone. Experiment II showed the English segments are approximately unitary: the natural background variation in segmental frequencies that arises within a single language variety is much larger than numerical differences across varieties. Variation in segmental frequencies seems to be driven by variation in discourse topic; topic-associated words cause bursts/lulls in local segmental frequencies. The article concludes with some methodological recommendations for comparing language samples.

scholarly journals Hypothesis testing for families of ergodic processes

Bernoulli ◽  
2006 ◽  
Vol 12 (2) ◽  
pp. 251-269 ◽  
Author(s):  
Andrew B. Nobel
Keyword(s):  
Hypothesis Testing ◽  
Ergodic Processes

scholarly journals Flow complexity in open systems: interlacing complexity index based on mutual information

2017 ◽  
Vol 825 ◽  
pp. 704-742 ◽  
Author(s):  
Jose M. Pozo ◽  
Arjan J. Geers ◽  
Maria-Cruz Villa-Uriol ◽  
Alejandro F. Frangi
Keyword(s):  
Mutual Information ◽  
Communication Systems ◽  
Communication Channel ◽  
Communication Theory ◽  
Open Systems ◽  
Straight Tube ◽  
Natural Distribution ◽  
Ergodic Processes ◽  
Complexity Index ◽  
Crucial Component

Flow complexity is related to a number of phenomena in science and engineering and has been approached from the perspective of chaotic dynamical systems, ergodic processes or mixing of fluids, just to name a few. To the best of our knowledge, all existing methods to quantify flow complexity are only valid for infinite time evolution, for closed systems or for mixing of two substances. We introduce an index of flow complexity coined interlacing complexity index (ICI), valid for a single-phase flow in an open system with inlet and outlet regions, involving finite times. ICI is based on Shannon’s mutual information (MI), and inspired by an analogy between inlet–outlet open flow systems and communication systems in communication theory. The roles of transmitter, receiver and communication channel are played, respectively, by the inlet, the outlet and the flow transport between them. A perfectly laminar flow in a straight tube can be compared to an ideal communication channel where the transmitted and received messages are identical and hence the MI between input and output is maximal. For more complex flows, generated by more intricate conditions or geometries, the ability to discriminate the outlet position by knowing the inlet position is decreased, reducing the corresponding MI. The behaviour of the ICI has been tested with numerical experiments on diverse flows cases. The results indicate that the ICI provides a sensitive complexity measure with intuitive interpretation in a diversity of conditions and in agreement with other observations, such as Dean vortices and subjective visual assessments. As a crucial component of the ICI formulation, we also introduce the natural distribution of streamlines and the natural distribution of world-lines, with invariance properties with respect to the cross-section used to parameterize them, valid for any type of mass-preserving flow.

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