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Equation 8 · Part 4 · The Statistical Mechanics of Irreversibility at Molecular Scale

fraction

⟨exp⁡(−ΔstotkB)⟩=1.\left\langle \exp\left(-\frac{\Delta s_{\mathrm{tot}}}{k_{\mathrm B}}\right) \right\rangle = 1.
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

The passage around this formula

Exponentiating and averaging over forward paths produces the integral fluctuation theorem, ⟨exp⁡(−ΔstotkB)⟩=1\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

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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