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Equation 5 · Part 3 · The Statistical Mechanics of Irreversibility at Molecular Scale

Symbol τ

Γ={xt}0τ\Gamma = \{x_t\}_{0}^{\tau}
τ\tau

What this part means

τ is an input to the expression that computes the quantity on the left.

Its job in the formula

τ is an input to the expression that computes the quantity on the left.

The passage around this formula

Consider a mesoscopic system coupled to a heat bath at temperature T . Its state xtx_t follows noisy dynamics under a time-dependent protocol λt\lambda_t . A trajectory over 0≤\le t≤\leτ\tau is denoted Γ\Gamma = \{xtx_t\}_{0}^{τ\tau} . The corresponding reverse experiment begins from the appropriate final ensemble, applies the reversed protocol, and generates a conjugate path Γ†\Gamma^\dagger .

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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