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Equation 10 · Part 3 · From Origins to Frontier: A History of Stochastic Thermodynamics and Complex Systems

=

⟨e−W/kBT⟩=e−ΔF/kBT\left\langle e^{-W/k_B T} \right\rangle = e^{-\Delta F/k_B T}
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

The next structural advance did not concern the demon at all; it concerned a much older and more general problem — how to extract equilibrium information from a process driven arbitrarily far from equilibrium. In 1997, Christopher Jarzynski published “Nonequilibrium Equality for Free Energy Differences” in Physical Review Letters [ 3 ] . The Jarzynski equality states that if a system is driven from one equilibrium state to another along some protocol, performing a fluctuating amount of work W on each repetition, the equilibrium free energy difference Δ\Delta F between the two states can be recovered exactly from an exponential average over the work distribution: ⟨e−W/kBT⟩=e−ΔF/kBT\left\langle e^{-W/k_B T} \right\rangle = e^{-\Delta F/k_B T}. This is a…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.