← Back to article

Equation 2 · The Statistical Mechanics of Irreversibility at Molecular Scale

What does this equation mean?

xtx_t

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

xtx_t

Symbol x_t

xtx_t is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Understand this part →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

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 .

Read the equation in its article →

For background, read the article’s source list.

Return to The Statistical Mechanics of Irreversibility at Molecular Scale

Browse the mathematical compendium →