As a first step in a larger study of student reasoning in upper-division thermal physics, we conducted thinkaloud interviews with 8 physics graduate students to probe their understanding of entropy. In this paper, we'll discuss results from a question which presented students with a novel system-a string in a bath of water-and asked students to rank the probabilities of particular arrangements of the string, define macrostates of the system, and discuss specifically what is meant by the entropy of the system. Exploring graduate students' understanding of entropy and their ability to solve problems and reason with entropic arguments will provide insights into how physicists develop a mature understanding of entropy as a physical quantity. We find a tendency for graduate students to project properties of macrostates onto constituent microstates, and discuss other observations. We identify connections to previous research and lay out the next steps for this project.

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In a prior study, we investigated graduate student reasoning on a set of entropy-related conceptual tasks in a think-aloud format. The tasks involved entropy from microscopic and macroscopic perspectives, ideal gases, and a novel context involving a system with a dynamic string. In the current study, we conducted interviews with undergraduates using the same questionnaire. Most students were interviewed during the second half of their upper-division Thermal Physics course at the University of Colorado Boulder while two were upper-division undergraduates from other institutions with strong physics programs. We analyze the responses of the undergraduates to a section of the interview involving a novel system of a dynamic string waving in a bath of water and discuss the similarities and differences between the undergraduate and graduate students' responses. The responses from the two populations share many similarities with a few noteworthy exceptions. The undergraduates generally did not produce multiple macrostate classifications in the novel system, and some expressed a concern with what they perceived to be an infinite number of microstates-and thus infinite entropy-which was not a concern among the graduate students.

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kinesin-II delays its recycling to the basal body and kinesin-II accumulates in a concentration gradient in the flagellum. As a result, kinesin-II is depleted at the flagellar base as the flagellum elongates. When the flagellum is elongated via Li þ treatment, or when the cell regrows flagella in the presence of protein synthesis inhibitor, the base is similarly depleted of kinesin-II. These results suggest that accumulation in the flagellum acts as a negative-feedback mechanism to limit the number of kinesin-II available for moving cargo on IFT trains, and limits the growth of flagella when they reach longer lengths.