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:

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:

This entry was posted on Friday, November 18th, 2016 at 3:50 pm and is filed under physics, probability. You can follow any responses to this entry through the RSS 2.0 feed.
You can leave a response, or trackback from your own site.

14 Responses to Jarzynksi on Non-Equilibrium Statistical Mechanics

I hadn’t seen the first one—thanks! The second is about the work of Jeremy England. He was invited to this workshop and indeed also to my own workshop on information and entropy in biological systems. But he doesn’t like to travel much, so he didn’t attend.

When I first encountered the Jarzynski equality and the fluctuation theorem, my first thought was “wow, these are amazing, why didn’t I learn them as an undergraduate?” and immediately following that was “wait, these were only discovered in the 1990s? Why was there a 63 year break in statistical mechanics progress between Nyquist & Onsager in 1928-1931 and Denis Evans & Christopher Jarzynski in 1994-1997?”

It is interesting workshop.
I am reading the Christopher Jarzynkski slides, and I am thinking that the basic process in thermodynamic is a piston moving in a heat engine, so that if someone simulate with a software a moving piston in a nanoscale engine (with some million of equal particles) using the collision of the molecules with an arbitrary velocity and an arbitrary acceleration of the piston (for a nonequilibrium state), then it could be possible to write an exact statistical law for this system using different initial conditions, and it could be possible to write the statistical law for a cycle based on the dynamic of the piston (a law from the parameter of the trajectory of the piston).

In Jarzynski’s context there is a description of the probability for a forward process relative to the probability of the reverse process (Eq. 31 in his Seminaire Poincare XV paper). That should have an immediate translation to your and Blake’s quantropy formalism. Right?

You can use Markdown or HTML in your comments. You can also use LaTeX, like this: $latex E = m c^2 $. The word 'latex' comes right after the first dollar sign, with a space after it. Cancel reply

You need the word 'latex' right after the first dollar sign, and it needs a space after it. Double dollar signs don't work, and other limitations apply, some described here. You can't preview comments here, but I'm happy to fix errors.

Great post. Have you seen this:

• Amanda Morris, Reconfiguring active particles into dynamic patterns,

Phys.org, 11 July 2016.and

• Natalie Wolchover, A new physics theory of life,

Quanta, 22 January 2014.I hadn’t seen the first one—thanks! The second is about the work of Jeremy England. He was invited to this workshop and indeed also to my own workshop on information and entropy in biological systems. But he doesn’t like to travel much, so he didn’t attend.

When I first encountered the Jarzynski equality and the fluctuation theorem, my first thought was “wow, these are amazing, why didn’t I learn them as an undergraduate?” and immediately following that was “wait, these were only discovered in the 1990s? Why was there a 63 year break in statistical mechanics progress between Nyquist & Onsager in 1928-1931 and Denis Evans & Christopher Jarzynski in 1994-1997?”

The lesson, I think, is that there’s a lot left to learn—and it’s wise to identify the regions where basic results haven’t been found yet!

Because there wasn’t.

Yes, there certainly wasn’t a “63 year break in statistical mechanics progress”. A lot occurred in that interval! I’ll just mention two earth-shakers:

1) The renormalization group analysis of second-order phase transitions, linking these phase transitions to quantum field theory.

2) Prigogine’s work on minimal entropy production for steady states near equilibrium, and his work on structure formation far from equilibrium.

It is interesting workshop.

I am reading the Christopher Jarzynkski slides, and I am thinking that the basic process in thermodynamic is a piston moving in a heat engine, so that if someone simulate with a software a moving piston in a nanoscale engine (with some million of equal particles) using the collision of the molecules with an arbitrary velocity and an arbitrary acceleration of the piston (for a nonequilibrium state), then it could be possible to write an exact statistical law for this system using different initial conditions, and it could be possible to write the statistical law for a cycle based on the dynamic of the piston (a law from the parameter of the trajectory of the piston).

It sounds like maybe you’re talking about ‘stochastic thermodynamics’

If Bob Dylan can’t accept the Nobel, maybe he can have Joan Baez accept it for him? Makes a little sense…

Maybe Joan can accept the task and delegate it to her cousin. At this point, that’s my best shot at getting my hands on a Nobel.

You underestimate yourself, possibly.

In Jarzynski’s context there is a description of the probability for a forward process relative to the probability of the reverse process (Eq. 31 in his Seminaire Poincare XV paper). That should have an immediate translation to your and Blake’s quantropy formalism. Right?

(Check spelling of Jarzynski in the title.)

Fun question, but I have no idea as to the answer!

[…] John Baez’s excellent coverage of Jarzynksi. […]