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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...
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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.
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The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
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A living cell's primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers in the universe are completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that...
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Multiscale entropy rate analysis of complex mobile agents.

Tuhin Paul1, Kevin G Stanley1, Nathaniel D Osgood1

  • 1Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada.

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|November 27, 2018
PubMed
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Predicting object motion is challenging for complex systems. This study derives a general law to measure mobility entropy rate, enabling comparisons across diverse datasets and revealing novel insights into movement patterns.

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Lempel–Ziv entropyhuman mobility modelmobility entropy rate

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Area of Science:

  • Physics
  • Complex Systems
  • Information Theory

Background:

  • Predicting object motion is a fundamental scientific challenge, especially for systems with agency.
  • Existing models struggle with complex or history-dependent motion patterns.
  • Information entropy rate offers a theoretical limit on predictability but is resolution-dependent.

Purpose of the Study:

  • To derive a general law relating mobility entropy rate to spatial/temporal resolutions and path properties.
  • To develop a method for correcting motion data for resolution effects.
  • To enable robust comparison of mobility entropy rates across diverse datasets.

Main Methods:

  • Derivation of a closed-form law for mobility entropy rate.
  • Regression analysis to correct for spatial and temporal resolution effects.
  • Application of the derived measure to empirical datasets.

Main Results:

  • A novel, dimension-robust measure of mobility entropy rate was developed.
  • The method allows for the comparison of mobility entropy rates across different datasets.
  • Analysis revealed similarities between taxicabs and drifters, predictable undergraduate movements, and Canadian moose browsing patterns.

Conclusions:

  • The derived law and corrected measure provide a powerful tool for analyzing complex motion patterns.
  • This approach offers new insights into the predictability and underlying dynamics of various moving entities.
  • The findings highlight the universality of movement principles across seemingly disparate systems.