In macroscopic thermodynamics, the second law is often summarized categorically: heat does not spontaneously pass from a cooler body to a warmer one. Yet in very small systems observed over extremely short intervals, random molecular motion can briefly produce such transfers. The fluctuation theorem both predicts these reversals and shows, within the same probabilistic framework, that they become vanishingly unlikely as system size and observation time increase. Macroscopic irreversibility is therefore not an independent rule merely overlaid on the microscopic account. The theorem _____ the second law’s large-scale reliability in the statistics that also permit brief, small-scale reversals.
Which choice completes the text with the most logical and precise word or phrase?
For a difficult words-in-context question, determine not only the passage’s broad position but also the exact relationship named by the sentence containing the blank. Distinguish among explaining a claim’s basis, restating it, limiting it, and obscuring it by checking the object of the blank and the logical role of the preceding evidence.
Hints
Track the explanatory relationship
Ask whether the theorem merely rephrases the macroscopic rule or explains why that rule is reliable.
Use the preceding sentence
The same framework accounts for both small-scale reversals and their disappearance at larger scales. Look for a word indicating that one account supplies the basis for another.
Step-by-step Explanation
Identify the apparent tension
Brief reversals of heat flow are possible in very small systems, even though the second law reliably describes macroscopic behavior.
Determine how the theorem addresses the tension
The theorem does not merely express the macroscopic rule in different terms. By showing that reversals become vanishingly unlikely as scale increases, it explains why large-scale irreversibility follows from the underlying probabilities.
Choose the precise relationship
To ground a claim in something is to provide its basis or justification. Because microscopic statistics provide the basis for the second law’s large-scale reliability, grounds is the most precise choice.