• Jarza Jarzynski Equality pixel-art physics T-shirt, white tee, front view

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Jarza

The Jarzynski Equality Physics

\[\langle e^{-\beta W}\rangle = e^{-\beta\Delta F}, \qquad \beta = \frac{1}{k_B T}\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Jarza pulls a molecular rope again and again. Some pulls cost less than the free energy. Average them the right way and the answer comes out exact.

The Physics

Pulling a small system out of equilibrium, the work W varies from run to run. The Jarzynski equality says the exponential average of that work gives the equilibrium free-energy difference exactly. Individual pulls can come in below ΔF; on average W ≥ ΔF still holds.

⟨e^(−βW)⟩ = e^(−βΔF), β = 1/(k_B T)

  • W: work done in one run (J)
  • ΔF: free-energy difference (J)
  • β: inverse thermal energy (1/J)
  • k_B: Boltzmann constant (J/K)
  • T: temperature (K)
  • ⟨ ⟩: average over many runs

C. Jarzynski published it in 1997, G. Crooks generalised it in 1999, and Liphardt et al. tested it by pulling single RNA molecules (Science, 2002).

Honest caveat: It is not a second-law violation, and it needs the system to start in equilibrium.

On the shirt

Front: Jarza, the pixel-art character, with the title. Back: the equality, the Crooks relation, the below-ΔF note and the 1997, 1999 and 2002 sources. Printed on a unisex tee.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

크기 비교: M 사이즈는 폭이 20 in (50.80 cm)로, 약 3.143 × 1034 플랑크 길이입니다(lP = 1.616255 × 10−35 m). 줄자가 더 빠릅니다.

Measurements in inches, ±1.5 in tolerance.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

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The physics

I pull a molecular rope again and again. Some pulls cost less than the free energy. Average them the right way and the answer comes out exact.

Drag a small system out of equilibrium and the work W changes from run to run. Christopher Jarzynski showed in 1997 that the exponential average of that work, ⟨e^(−βW)⟩, equals e^(−βΔF), so the equilibrium free-energy difference can be read from pulls as fast as you like. Gavin Crooks sharpened it in 1999 by comparing forward and time-reversed pulls. In 2002 Liphardt and colleagues tested it by unfolding single RNA hairpins.

No law is broken: on average ⟨W⟩ ≥ ΔF still holds, even though single pulls can come in below ΔF. And it needs the system to start in equilibrium.

Equations

\[\langle e^{-\beta W}\rangle = e^{-\beta\Delta F}, \qquad \beta = \frac{1}{k_B T}\]
\[\frac{P_F(W)}{P_R(-W)} = e^{\beta(W - \Delta F)}\]
SymbolMeaningUnit
\(W\) work done on the system in one run \(\mathrm{J}\)
\(\langle\cdots\rangle\) average over many runs started from equilibrium \(\mathrm{1}\)
\(\Delta F\) equilibrium (Helmholtz) free-energy difference \(\mathrm{J}\)
\(\beta\) inverse thermal energy \(\mathrm{1/J}\)
\(k_B\) Boltzmann constant, 1.380 649 × 10⁻²³ J/K (exact) \(\mathrm{J/K}\)
\(T\) bath temperature \(\mathrm{K}\)
\(P_F(W)\) probability density of work in forward runs \(\mathrm{1/J}\)
\(P_R(-W)\) probability density of work −W in time-reversed runs \(\mathrm{1/J}\)

Sources

  1. Jarzynski (1997) Nonequilibrium Equality for Free Energy Differences, Phys. Rev. Lett. 78, 2690
  2. Crooks (1999) Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Phys. Rev. E 60, 2721
  3. Liphardt et al. (2002) Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski's Equality, Science 296, 1832

Field notes

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