Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Entropy02:39

Entropy

33.7K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
33.7K
Entropy01:18

Entropy

3.3K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.3K
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.0K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.0K
Sample Size Calculation01:19

Sample Size Calculation

5.7K
Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...
5.7K
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

4.0K
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
4.0K
Standard Entropy Change for a Reaction03:00

Standard Entropy Change for a Reaction

23.0K
Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
23.0K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Statistical errors undermine claims about the evolution of polysynthetic languages.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Still No Evidence for an Effect of the Proportion of Non-Native Speakers on Natural Language Complexity.

Entropy (Basel, Switzerland)·2024
Same author

Languages with more speakers tend to be harder to (machine-)learn.

Scientific reports·2023
Same author

A large quantitative analysis of written language challenges the idea that all languages are equally complex.

Scientific reports·2023
Same author

Is More Always Better? Testing the Addition Bias for German Language Statistics.

Cognitive science·2023
Same author

Testing the Relationship between Word Length, Frequency, and Predictability Based on the German Reference Corpus.

Cognitive science·2022

Related Experiment Video

Updated: Nov 27, 2025

Lexical Decision Task for Studying Written Word Recognition in Adults with and without Dementia or Mild Cognitive Impairment
06:48

Lexical Decision Task for Studying Written Word Recognition in Adults with and without Dementia or Mild Cognitive Impairment

Published on: June 25, 2019

9.5K

Studying Lexical Dynamics and Language Change via Generalized Entropies: The Problem of Sample Size.

Alexander Koplenig1, Sascha Wolfer1, Carolin Müller-Spitzer1

  • 1Department of Lexical Studies, Institute for the German language (IDS), 68161 Mannheim, Germany.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

Generalized entropies quantify text similarity by analyzing word frequencies. However, these measures are sensitive to text length, complicating the study of language change and lexical dynamics.

Keywords:
Jensen–Shannon divergenceZipf’s lawgeneralized divergencegeneralized entropysample sizetext length

More Related Videos

Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

1.2K
Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language
09:27

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language

Published on: October 13, 2018

10.4K

Related Experiment Videos

Last Updated: Nov 27, 2025

Lexical Decision Task for Studying Written Word Recognition in Adults with and without Dementia or Mild Cognitive Impairment
06:48

Lexical Decision Task for Studying Written Word Recognition in Adults with and without Dementia or Mild Cognitive Impairment

Published on: June 25, 2019

9.5K
Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

1.2K
Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language
09:27

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language

Published on: October 13, 2018

10.4K

Area of Science:

  • Quantitative linguistics
  • Information theory
  • Computational linguistics

Background:

  • Generalized entropies offer a method to quantify symbol sequence similarity.
  • Textual data analysis is complicated by Zipf's law, where word frequencies follow a power-law distribution.
  • Understanding lexical dynamics requires robust similarity measures.

Purpose of the Study:

  • To systematically and empirically study the application of generalized entropies for analyzing lexical dynamics.
  • To investigate the impact of sample size on similarity measures based on generalized entropies.
  • To assess the suitability of these measures for studying language change.

Main Methods:

  • Analysis of lexical dynamics using generalized entropies of order α.
  • Empirical study on a large corpus of German text from "Der Spiegel" (1947-2017).
  • Investigation of the influence of text length (sample size) on similarity measures.

Main Results:

  • Similarity measures based on generalized entropies are heavily dependent on sample size (text length).
  • This dependence poses challenges for quantifying lexical dynamics and language change.
  • Standard sampling techniques do not resolve the issue of sample size dependency.

Conclusions:

  • The sample size dependency of generalized entropies limits their direct application in analyzing language change.
  • Further research is needed to develop methods that account for or mitigate this dependency.
  • The findings have significant implications for the statistical analysis of natural languages.