Here at the Santa Fe Institute we’re having a workshop on Statistical Physics, Information Processing and Biology. Unfortunately the talks are not being videotaped, so it’s up to me to spread the news of what’s going on here.
where is Boltzmann’s consstant and is the temperature of a system that’s in equilibrium before some work is done on it. is the change in free energy, is the amount of work, and the angle brackets represent an average over the possible options for what takes place—this sort of process is typically nondeterministic.
We’ve seen a good quick explanation of this equation here on Azimuth:
• Eric Downes, Crooks’ Fluctuation Theorem, Azimuth, 30 April 2011.
We’ve also gotten a proof, where it was called the ‘integral fluctuation theorem’:
• Matteo Smerlak, The mathematical origin of irreversibility, Azimuth, 8 October 2012.
It’s a fundamental result in nonequilibrium statistical mechanics—a subject where inequalities are so common that this equation is called an ‘equality’.
Two days ago, Jarzynski gave an incredibly clear hour-long tutorial on this subject, starting with the basics of thermodynamics and zipping forward to modern work. With his permission, you can see the slides here:
• Christopher Jarzynski, A brief introduction to the delights of non-equilibrium statistical physics.
Also try this review article:
• Christopher Jarzynski, Equalities and inequalities: irreversibility and the Second Law of thermodynamics at the nanoscale, Séminaire Poincaré XV Le Temps (2010), 77–102.