Equation 8 · Part 5 · The Statistical Mechanics of Irreversibility at Molecular Scale

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\left\langle \exp\left(-\frac{\Delta s_{\mathrm{tot}}}{k_{\mathrm B}}\right) \right\rangle = 1.

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What this part means

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Its job in the formula

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

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The passage around this formula

Exponentiating and averaging over forward paths produces the integral fluctuation theorem, $\left\langle \exp\left(-\frac{\Delta s_{\mathrm{tot}}}{k_{\mathrm B}}\right) \right\rangle = 1$ . Jensen’s inequality then gives

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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