Equation 5 · The Statistical Mechanics of Irreversibility at Molecular Scale
What does this equation mean?
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 equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol Gamma
Gamma is part of the quantity the equation computes from the expression on the right.
Symbol x_t
is an input to the expression that computes the quantity on the left.
Symbol τ
τ is an input to the expression that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →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.
superscript
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.
See an illustrated explanation →How to interpret it
Read it 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 follows noisy dynamics under a time-dependent protocol . A trajectory over 0 t is denoted = \{\}_{0}^{} . The corresponding reverse experiment begins from the appropriate final ensemble, applies the reversed protocol, and generates a conjugate path .
For background, read the article’s source list.
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