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