Equation 5 · Part 4 · The Statistical Mechanics of Irreversibility at Molecular Scale

=

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

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.

Full expression=Article meaning

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 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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