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Physics in the Science of Complex Systems - Draft 0

Module by: Ketel Turzo

Summary: physics course for non-physicist complex systems researchers

Physics in the Science of Complex Systems – Draft 0

The lectures are organized in lessons within thematic courses.

General introduction

Thermal and statistical physics

The main chapters are copied from the courses of Harvey Gould and Jan Tobochnik, Clark University, Worcester, MA, USA. If not, the source is precised into brackets.

http://stp.clarku.edu/ notes/

1.1 From Microscopic to Macroscopic Behavior: Statistical Physics

Lesson 1
  • Introduction
  • Some qualitative observations
  • Doing work
  • Quality of energy
Lesson 2
  • Some simple simulations
  • Work, heating, and the first law of thermodynamics
  • The fundamental need for statistical approach
  • Time and ensemble averages
Lesson 3
  • Models of matter

The ideal gas

Interparticle potentials

Lattice models

  • Importance of simulations
  • Summary

Additional problems

Suggestions for further reading

1.2 Thermodynamic Concepts

Lesson 4
  • Introduction
  • The system
  • Thermodynamic equilibrium
  • Temperature
  • Pressure equation of state
Lesson 5
  • Some thermodynamic processes
  • Work
  • The first law of thermodynamics
  • Energy equation of state
Lesson 6
  • Heat capacity and enthalpy
  • Adiabatic processes
  • The second law of thermodynamics
  • The thermodynamic temperature
Lesson 7
  • The second law and heat engine
  • Entropy changes
  • Equivalence of thermodynamic and ideal gas scale temperatures
  • The thermodynamic pressure
Lesson 8
  • The fundamental thermodynamic relation
  • The entropy of an ideal gas
  • The third law of thermodynamics
  • Free energies

Additional problems

Suggestions for further reading

1.3 Statistical Mechanics

Lesson 9
  • Introduction
  • A simple example of a thermal interaction
  • Counting microstates

Non-interacting spins

One-dimensional Ising model

A particle in a one-dimensional box

One-dimensional harmonic oscillator

A particle in a two-dimensional box

Two non-interacting identical particles and the semi-classical limit

Lesson 10

  • The number of states of N non-interacting particles: semi- classical limit
  • The microcanonical ensemble (fixed E, V, and N)
  • Systems in contact with a heat bath: the canonical ensemble (fixed T, V, and N)
  • Connection between statistical mechanics and thermodynamics
Lesson 11
  • Simple applications of the canonical ensemble
  • Example of a simple thermometer
  • Simulations of the microcanonical ensemble
  • Simulations of the canonical ensemble
Lesson 12
  • Grand canonical ensemble (fixed T, V, and )
  • Entropy and disorder
  • The volume of a hypersphere
  • Fluctuations in the canonical ensemble
  • Molecular dynamics

(Course from North Carolina State University, Raleigh, NC, USA:

http://chsfpc5.chem.ncsu.edu/~franzen/ CH795N/lecture/IV/IV.html)

Additional problems

Suggestions for further reading

1.4 Thermodynamic Relations and Processes

Lesson 13

1.4.1 Introduction

1.4.2 Maxwell relations

1.4.3 Applications of the Maxwell relations

Internal energy of an ideal gas

Relation between the specific heats

Lesson 14

1.4.4 Applications to irreversible processes

The Joule or free expansion process

Joule-Thomson process

  • Equilibrium between phases

Equilibrium conditions

Clausius-Clapeyron equation

Simple phase diagrams

Pressure dependence of the melting point

Pressure dependence of the boiling point

The vapor pressure curve

Lesson 15

  • Lattice gas and Ising model

(Introduction to lattice gas from Victor Batista, Chemistry department, Yale University, New Haven, NE, USA:

http://xbeams.chem.yale.edu/~batista/vaa/ node38.html)

(Applet of ising model, from A. Peter young, Physics department, University of California, San Diego, CA, USA:

http://bartok.ucsc.edu/peter/java/ising/keep/ ising.html)

  • Phase transitions

(Generalities from Wikipedia:

http://en.wikipedia.org/wiki/ Phase_transition)

  • A geometric phase transition: percolation

(Lectures notes from the MIT NSE Virtual Reading Room, Massachusetts Institute of Technology, Cambridge, MA, USA:

http:// mightylib.mit.edu/Course%20Materials/22.00/Spring%202002/Notes/lecture_3.pdf )

Lesson 16
  • Brownian motion

(Introduction from the physics department of the University of Queensland, Brisbane, Australia:

http://www.physics.uq.edu.au/people/mcintyre/ php/laboratories/download_file.php?eid=38)

  • Chaos and self-organization

(Introduction to chaos theory from the center of complex quantum systems, University of Texas, Austin, TX, USA:

http:// order.ph.utexas.edu/

Generalities from Wikipedia:

http://en.wikipedia.org/wiki/Self- organization)

Lesson 17
  • Fractals

(Introduction from Michael Frame, Benoit Mandelbrot, and Nial Neger, Yale University, New Haven, NE, USA:

http://classes.yale.edu/Fractals/)

  • Sand Piles

(Introduction from Benoît Masson, Laboratoire Informatique Signaux et systèmes of Sofia Antipolis, France, EU:

http://www.i3s.unice.fr/~bmasson/eng/piles1.php)

  • Spin glasses

(Short introduction & references from Daniel Stariolo, Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil:

http://www.if.ufrgs.br/~stariolo/spinglasses.html)

Additional problems

Suggestions for further reading

Quantum physics made relatively simple

Hans Bethe, Cornell University, Ithaca, NY, USA

Presentation of quantum theory and mechanics through their histories.

http://bethe.cornell.edu

3 courses of about 45-50 mn

Video and audio versions

Slides are presented in parallel to the video documents

2.1 “Old Quantum Theory”: 1900 – 1915

2.2 Quantum Mechanics: 1924 – 1928

2.3 Interpretation works on the wave function, the Heisenberg Uncertainty Principle, and the Pauli Exclusion Principle

Suggestions for further reading

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