The Cartesian Cafe

Daniel Schroeder is a particle and accelerator physicist and an editor for The American Journal of Physics. Dan received his PhD from Stanford University, where he spent most of his time at the Stanford Linear Accelerator, and he is currently a professor in the department of physics and astronomy at Weber State University. Dan is also the author of two revered physics textbooks, the first with Michael Peskin called An Introduction to Quantum Field Theory (or simply Peskin & Schroeder within the physics community) and the second An Introduction to Thermal Physics. Dan enjoys teaching physics courses at all levels, from Elementary Astronomy through Quantum Mechanics.

In this episode, I get to connect with one of my teachers, having taken both thermodynamics and quantum field theory courses when I was a university student based on Dan's textbooks. We take a deep dive towards answering two fundamental questions in the subject of thermodynamics: what is temperature and what is entropy? We provide both a qualitative and quantitative analysis, discussing good and bad definitions of temperature, microstates and macrostates, the second law of thermodynamics, and the relationship between temperature and entropy. Our discussion was also a great chance to shed light on some of the philosophical assumptions and conundrums in thermodynamics that do not typically come up in a physics course: the fundamental assumption of statistical mechanics, Laplace's demon, and the arrow of time problem (Loschmidt's paradox) arising from the second law of thermodynamics (i.e. why is entropy increasing in the future when mechanics has time-reversal symmetry).

Patreon: https://www.patreon.com/timothynguyen

Outline:

• 00:00:00 : Introduction
• 00:01:54 : Writing Books
• 00:06:51 : Academic Track: Research vs Teaching
• 00:11:01 : Charming Book Snippets
• 00:14:54 : Discussion Plan: Two Basic Questions
• 00:17:19 : Temperature is What You Measure with a Thermometer
• 00:22:50 : Bad definition of Temperature: Measure of Average Kinetic Energy
• 00:25:17 : Equipartition Theorem
• 00:26:10 : Relaxation Time
• 00:27:55 : Entropy from Statistical Mechanics
• 00:30:12 : Einstein solid
• 00:32:43 : Microstates + Example Computation
• 00:38:33: Fundamental Assumption of Statistical Mechanics (FASM)
• 00:46:29 : Multiplicity is highly concentrated about its peak
• 00:49:50 : Entropy is Log(Multiplicity)
• 00:52:02 : The Second Law of Thermodynamics
• 00:56:13 : FASM based on our ignorance?
• 00:57:37 : Quantum Mechanics and Discretization
• 00:58:30 : More general mathematical notions of entropy
• 01:02:52 : Unscrambling an Egg and The Second Law of Thermodynamics
• 01:06:49 : Principle of Detailed Balance
• 01:09:52 : How important is FASM?
• 01:12:03 : Laplace's Demon
• 01:13:35 : The Arrow of Time (Loschmidt's Paradox)
• 01:15:20 : Comments on Resolution of Arrow of Time Problem
• 01:16:07 : Temperature revisited: The actual definition in terms of entropy
• 01:25:24 : Historical comments: Clausius, Boltzmann, Carnot
• 01:29:07 : Final Thoughts: Learning Thermodynamics

Further Reading:

• Daniel Schroeder. An Introduction to Thermal Physics
• L. Landau & E. Lifschitz. Statistical Physics.

Twitter: @iamtimnguyen

Webpage: http://www.timothynguyen.org