# Statistics in physics

What are the uses of statistics in physics? I am about to embark upon a study of statistics and I would like to know what the particular benefits I gain in physics.

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Statistics are used in physics to provide a conceptual link between the 'macroscopic view' and the 'microscopic view'. For example, when studying gases, we can examine the statistical distribution of particle velocities and energies to gain an understanding of the relationship between the macroscopically observable quantities (pressure, volume & temperature) and the 'unobserved' or 'internal' (molecular-level) energies and velocity of individual particles which make up the gas. Maxwell-Boltzmann statistics are used to describe the distribution of particles at different energy levels as a function of temperature. This has can be used to gain insight into a wide range of processes such as diffusion.

Applying a statistical approach to thermodynamics can lead to a deeper understanding concepts such as temperature and entropy. For example, temperature can be understood statistically, as the average kinetic energy of atoms in a bulk material.

The statistical approach to thermodynamics produces some useful insights and applications in apparently unrelated fields such as encryption, communications and information theory through the development of an 'abstract' concept of entropy as a measure of uncertainty in a random variable.

The application of statistics to describe random (stochastic) processes such as Brownian motion has also proven useful in the derivation of the 'path integral' formulation of quantum physics.

Also in quantum physics, the application of statistics yields some fascinating results. Specifically, the statistical analysis of bosons (subatomic particles with integer spin) is can be described using Bose-Einstein statistics which has applications in a wide range of fields from superconductors, lasers and very low helium (condensed matter physics).

Applying statistics to fermions (subatomic particles such as electrons, which obey the Pauli Exclusion Principle) yields the Fermi-Dirac statistics which are used in the description of conductivity of metals and semiconductors and has application in the development of solid-state electronics devices such as transistors and integrated circuits.

On a broader level, the study of statistics provides a practical set of tools for testing hypotheses and estimating confidence intervals on aggregate data, not only in physics, but in all the scientific disciplines. In this sense, it forms the basis for the proper design of experiments, interpretation (significance) of data and correlation of information which ultimately underpins the development of modern scientific knowledge.

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Another interesting use for statistical physics is to describe actual phase transitions. Thought I'd add that one to the list. –  Wouter Jan 15 '13 at 12:22

Regression is used everywhere where numerical data must be analyzed.

Statistical mechanics is applied large deviation theory.

Quantum physics is noncommutative probability theory and statistics.

Turbulence is stochastic PDE in space-time.

Quantum field theory is analytically continued stochastic processes in infinite-dimesnional spaces.

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Very intresting answer. That clarifies alot to me. Although it might be because im on math.stackexchange :) –  mick Dec 5 '13 at 20:11

I can't vouch for your school, but I would imagine that the kind of statistics you do in a Statistics Major is different from the statistics used in thermodynamics. Thermodynamics is basically ensemble theory, permutations and expectation values.

I imagine that in a pure Statistics course, you will daily hear words like "Set theory, Bayesian, correlation, confidence level, Monte Carlo, Maximum Likelihood, Probability Networks. This is more the stuff that is needed for Data evaluation. You might find yourself among the physicists at CERN one day.

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Landau in his famous letter explaining what mathematics is necessary for physicists have definitely expressed that all physicists need from statistics they get during the lectures on statistical mechanics. Form my experience I confirm that that is 100% true.

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