Distance in Information and Statistical Physics III

Takuya Yamano1

  • 1Faculty of Science, Kanagawa University, 2946, 6-233 Tsuchiya, Hiratsuka 259-1293, Japan.

Summary

This special issue revisits the concept of distance in information and statistical physics. It explores how distance metrics are fundamental to understanding complex systems and data analysis.

Related Concept Videos

Interference: Path Lengths01:10

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
1.4K
Distribution of Molecular Speeds01:27

Distribution of Molecular Speeds

The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
4.0K
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
1.6K
Mean free path and Mean free time01:22

Mean free path and Mean free time

Consider the gas molecules in a cylinder. They move in a random motion as they collide with each other and change speed and direction. The average of all the path lengths between collisions is known as the "mean free path."
3.9K
The Uncertainty Principle04:08

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
23.5K
Correlation of Experimental Data01:23

Correlation of Experimental Data

Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity,...
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