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

Probability Distributions01:32

Probability Distributions

12.2K
 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...
12.2K
Poisson Probability Distribution01:09

Poisson Probability Distribution

12.1K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
12.1K
Binomial Probability Distribution01:15

Binomial Probability Distribution

15.9K
A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
15.9K
Probability Laws01:49

Probability Laws

44.4K
Overview
44.4K
Probability in Statistics01:14

Probability in Statistics

23.4K
Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
23.4K
Probability Histograms01:17

Probability Histograms

13.3K
A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
13.3K

You might also read

Related Articles

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

Sort by
Same author

Maximum entropy and constraints in composite systems.

Physical review. E·2022
Same author

Entropy production and volume contraction in thermostated Hamiltonian dynamics.

Physical review. E·2018
Same author

General formalism for singly thermostated Hamiltonian dynamics.

Physical review. E, Statistical, nonlinear, and soft matter physics·2015
Same author

Similarity-based constitutive relations for local mass fluxes in incompressible mixing layers.

Physical review. E, Statistical, nonlinear, and soft matter physics·2006
Same author

Linearized stability analysis of accelerated planar and spherical fluid interfaces with slow compression.

Physical review. E, Statistical, nonlinear, and soft matter physics·2003

Related Experiment Video

Updated: Feb 4, 2026

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat
11:18

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Published on: September 12, 2014

15.8K

Supercanonical probability distributions.

John D Ramshaw1

  • 1Department of Physics, Portland State University, Portland, Oregon 97207, USA.

Physical Review. E
|September 27, 2018
PubMed
Summary

Finite heat baths modify canonical probability distributions. Truncating entropy expansions yields supercanonical distributions, including power-law forms that approximate the Tsallis distribution for finite systems.

Area of Science:

  • Statistical Mechanics
  • Thermodynamics
  • Information Theory

Background:

  • Canonical probability distribution describes systems in thermal equilibrium with infinite heat baths.
  • Finite heat baths introduce modifications to this standard distribution.
  • Previous methods for deriving these modifications involved truncating Taylor series expansions of heat bath entropy.

Purpose of the Study:

  • To investigate modifications to the canonical probability distribution when a heat bath is finite.
  • To explore different forms of supercanonical distributions arising from entropy expansion truncations.
  • To clarify the relationship between these derived distributions and the Tsallis distribution.

Main Methods:

  • Considered Taylor-series expansions of the heat bath entropy.

More Related Videos

Assessment of Open Probability of the Mitochondrial Permeability Transition Pore in the Setting of Coenzyme Q Excess
07:35

Assessment of Open Probability of the Mitochondrial Permeability Transition Pore in the Setting of Coenzyme Q Excess

Published on: June 1, 2022

2.6K
Modified Most Probable Number Assay to Quantify Salmonella in Raw and Ready-to-Cook Chicken Products
08:19

Modified Most Probable Number Assay to Quantify Salmonella in Raw and Ready-to-Cook Chicken Products

Published on: January 31, 2025

1.0K

Related Experiment Videos

Last Updated: Feb 4, 2026

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat
11:18

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Published on: September 12, 2014

15.8K
Assessment of Open Probability of the Mitochondrial Permeability Transition Pore in the Setting of Coenzyme Q Excess
07:35

Assessment of Open Probability of the Mitochondrial Permeability Transition Pore in the Setting of Coenzyme Q Excess

Published on: June 1, 2022

2.6K
Modified Most Probable Number Assay to Quantify Salmonella in Raw and Ready-to-Cook Chicken Products
08:19

Modified Most Probable Number Assay to Quantify Salmonella in Raw and Ready-to-Cook Chicken Products

Published on: January 31, 2025

1.0K
  • Analyzed two distinct expansion parameter choices.
  • Derived supercanonical distributions based on these truncations.

    • Main Results:

    • Two forms of supercanonical distributions were derived: exponential and power-law.
    • The power-law form was found to be identical in structure to the Tsallis distribution.
    • The Tsallis distribution is shown to be a valid asymptotic approximation for any finite heat bath.

    Conclusions:

    • The form of modified probability distributions for finite heat baths depends on the chosen entropy expansion parameter.
    • The Tsallis distribution emerges as a general asymptotic approximation for finite heat baths, independent of specific system details.
    • The study clarifies that the Tsallis distribution's validity in this context is mathematical, not based on an intrinsic link to Tsallis entropy itself.