← All parts of this equation

Equation 6 · Part 9 · The Arrow of Time and the Engine of Evolution

subscript

⟨e−βW⟩=e−βΔF,β=1kBT\left\langle e^{-\beta W} \right\rangle = e^{-\beta \Delta F}, \qquad \beta = \frac{1}{k_{\mathrm{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

Christopher Jarzynski’s 1997 equality was the opening result. For a system beginning in thermal equilibrium and then driven away from it by an arbitrarily fast, arbitrarily far-from-equilibrium protocol, the exponential average of the work W performed on it recovers the equilibrium free-energy difference Δ\Delta F between the protocol’s start and end points exactly: ⟨e−βW⟩=e−βΔF,β=1kBT\left\langle e^{-\beta W} \right\rangle = e^{-\beta \Delta F}, \qquad \beta = \frac{1}{k_{\mathrm{B}} T}. [ 5 ] . The result does not say average work equals Δ\Delta F — dissipation makes the ordinary average of W larger than Δ\Delta F whenever the protocol is not quasistatic — it says a specific nonlinear average of a driven, dissipative, irreversible process reproduces an equilibrium quantity exactly, which is a…

Read this part in the article →

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.