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Equation 10 · Part 5 · From Origins to Frontier: A History of Stochastic Thermodynamics and Complex Systems

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

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