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Statistical Physics and ThermodynamicsAn Introduction to Key Concepts$
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Jochen Rau

Print publication date: 2017

Print ISBN-13: 9780199595068

Published to Oxford Scholarship Online: November 2017

DOI: 10.1093/oso/9780199595068.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 03 August 2021

Simple Systems

Simple Systems

Chapter:
(p.57) 4 Simple Systems
Source:
Statistical Physics and Thermodynamics
Author(s):

Jochen Rau

Publisher:
Oxford University Press
DOI:10.1093/oso/9780199595068.003.0004

Even though the general framework of statistical mechanics is ultimately targeted at the description of macroscopic systems, it is illustrative to apply it first to some simple systems: a harmonic oscillator, a rotor, and a spin in a magnetic field. These applications serve to illustrate how a key function associated with the Gibbs state, the so-called partition function, is calculated in practice, how the entropy function is obtained via a Legendre transformation, and how such systems behave in the limits of high and low temperatures. After discussing these simple systems, this chapter considers a first example where multiple constituents are assembled into a macroscopic system: a basic model of a paramagnetic salt. It also investigates the size of energy fluctuations and how—in the case of the paramagnet—these fluctuations scale with the number of constituents.

Keywords:   harmonic oscillator, rotor, spin, magnetic field, paramagnet, partition function, Legendre transformation, high-temperature limit, low-temperature limit, fluctuations

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