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.