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Foundations of Statistical Mechanics
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Module 2
Kinetic Theory and the Approach to Equilibrium
From Phase-Space to Transport: The Boltzmann Equation
Define the one-particle distribution function and derive the Boltzmann transport equation from phase-space continuity and collision considerations.
2
Maxwell-Boltzmann Distribution: Stationary, Collisionless Solution to the Boltzmann Equation
Show that the Maxwell-Boltzmann distribution is the stationary, collisionless solution to the Boltzmann equation.
3
Boltzmann's H-Theorem: Irreversibility and the Arrow of Time
State and prove Boltzmann's H-theorem and discuss its implications for irreversibility and the arrow of time.
4
Resolving Paradoxes: Loschmidt, Zermelo, and the H-theorem
Explain the resolution of the Loschmidt (reversibility) and Zermelo (recurrence) paradoxes in the context of the H-theorem.
5
Solving the Boltzmann Equation in the Relaxation-Time Approximation
Solve the Boltzmann equation in the relaxation-time approximation for a system under a small external perturbation.
6
Transport Coefficients from the Relaxation-Time Approximation
Apply the relaxation-time approximation to derive expressions for transport coefficients like thermal conductivity and viscosity.
Previous module
Information, Probability, and Asymptotic Methods
Next module
Foundations of Equilibrium Statistical Mechanics