Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Choosing Between z and t Distribution

Choosing Between z and t Distribution

The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution to use for a calculation, one needs to determine the sample size, the nature of the distribution, and whether the population standard deviation is known. If the population standard deviation is known and the population is normally distributed, or if the sample size is greater than 30, the z distribution is preferred. The Student t distribution is...

Distributions to Estimate Population Parameter

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...

Probability Distributions

Probability Distributions

The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...

Estimating Population Mean with Unknown Standard Deviation

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...

Extraction: Partition and Distribution Coefficients

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an organic...

Student t Distribution

Student t Distribution

The population standard deviation is rarely known in many day-to-day examples of statistics. When the sample sizes are large, it is easy to estimate the population standard deviation using a confidence interval, which provides results close enough to the original value. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
The Student t distribution was developed by William S. Goset (1876–1937) of the...

You might also read

Related Articles

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

Sort by

Same author

<b>Catalog of the genus <i>Schmidtiana</i> Podaný 1971 (Coleoptera: Cerambycinae) in the Philippines with notes on species variation and key to the species</b>.

Zootaxa·2026

Same author

Long-Term Stable Neural Interfaces with Nanoporous Graphene Electrodes and Hybrid Polyimide-Aluminium Oxide Encapsulation.

Small methods·2025

Same author

A taxonomic revision of the Madagascar-endemic longhorn beetle genus Tsivoka Villiers (Coleoptera: Cerambycidae) with the description of a new species.

Zootaxa·2025

Same author

Double power-law universal scaling function for the distribution of waiting times in labquake catalogs.

Physical review. E·2025

Same author

Enhancement of the Elastocaloric Performance of Natural Rubber by Forced Air Convection.

Polymers·2024

Same author

Elastocaloric Waste/Natural Rubber Materials with Various Crosslink Densities.

Polymers·2023

Search research articles

Related Experiment Video

Updated: Jun 23, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Work distributions in the T=0 random field Ising model.

Xavier Illa¹, Josep Maria Huguet, Eduard Vives

¹Department of Applied Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Finland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 28, 2009

Summary

This study explores the random-field Ising model at zero temperature. A simple extension of the Crooks fluctuation theorem fails near the phase transition due to asymmetric distributions.

Related Experiment Videos

Last Updated: Jun 23, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Area of Science:

Statistical mechanics
Condensed matter physics
Computational physics

Background:

The random-field Ising model is a key model for understanding disordered magnetic systems.
The Crooks fluctuation theorem relates work and free energy changes in non-equilibrium processes.
Extending fluctuation theorems to zero temperature and quenched disorder presents theoretical challenges.

Purpose of the Study:

To investigate the applicability of the Crooks fluctuation theorem at zero temperature for the random-field Ising model.
To compare work distributions from non-equilibrium dynamics with internal energy distributions from equilibrium.
To understand the role of quenched disorder in modifying statistical mechanics theorems.

Main Methods:

Numerical simulations of the three-dimensional random-field Ising model.
Utilizing single-spin flip dynamics to generate metastable trajectories.
Analyzing work distributions along non-equilibrium paths and internal energy distributions along equilibrium paths.

Main Results:

Work and internal energy distributions exhibit significant asymmetry near the disordered-induced phase transition.
A straightforward extension of the Crooks fluctuation theorem is found to be inadequate at T=0 under these conditions.
The findings highlight limitations of standard fluctuation theorems in the presence of quenched disorder.

Conclusions:

The Crooks fluctuation theorem cannot be simply extended to zero temperature for the random-field Ising model with quenched disorder.
Asymmetric distributions near the phase transition are the primary reason for the theorem's failure.
Further theoretical developments are needed to address fluctuation theorems in disordered systems at low temperatures.