Equation 5 · Part 6 · The Statistical Mechanics of Irreversibility at Molecular Scale

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\Gamma = \{x_t\}_{0}^{\tau}

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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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The passage around this formula

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

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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