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Statistical mechanics has received limited attention in physics education research and remains a relatively underrepresented topic even in research on upper-division physics courses. The purpose of this study was to explore potential challenges that physics students encounter when they solve statistical mechanics problems in groups. Adopting a grounded approach, we video recorded and analyzed nine small student groups engaging in collaborative problem solving on the topic. The analysis involved iterative thematic coding, which gave rise to ten emergent categories of challenges. These were later divided into two broad groupings: challenges with concepts and challenges with problem-solving strategies. In the first grouping, we list seven identified categories related to the concepts of macrostates and microstates, distinguishable and indistinguishable particles, temperature, entropy, energy, equilibrium, heat bath, the Boltzmann distribution, and the partition function. In the second grouping, we list three categories related to the inappropriate application of common relations, difficulty managing tensions between calculated results and qualitative reasoning, and coming up with definitions of new and inconsistent concepts. Some of our findings are supported by existing research on the topic, and others are previously unreported. Based on our findings, we propose that future research should investigate the relations between the identified challenges on one hand, and students’ epistemological framing, reasoning, and use of multiple representations on the other. Finally, we suggest that teachers should spend time engaging students in a conceptual discussion of the central ideas of statistical mechanics, motivating the choice and pointing out limitations of commonly used toy models, and linking course content to real-world phenomena.

Idealized models are a natural part of physics research and education. In upper-division physics courses, which tend to be more abstract and sophisticated than the introductory courses, such simplified toy models often serve as pedagogical tools to illustrate concepts and calculations. In the topic of statistical mechanics, we have studied the challenges faced by small problem-solving groups of upper-division students. Our findings indicate that students struggle to recognize the underlying structure of commonly used toy models. Students faced various pitfalls as they tended to rely on surface features of the tasks, in combination with loosely connected ideas about key concepts. Based on our findings, we discuss recommendations for teachers in statistical mechanics and other advanced courses that resort to simplified models to explain complex concepts.

Intuition has been reported as being pivotal in guiding students' problem solving. In this ongoing project, we employ a grounded approach to investigate how students use intuition during problem solving in beyond-intro chemistry and physics courses. We adopt a dynamic perspective on intuition, recognizing its context-dependency, to examine how students respond to their intuitions. In a case study, we inductively analyze existing video data of problem-solving sessions, and show that students' responses to intuition can be productive or unproductive, regardless of the intuition's "correctness". This highlights the need to equip students with strategies to manage their intuitions productively. Based on our findings, we recommend teachers to: adopt a flexible stance toward intuition; explicitly incorporate the topic of intuition in classroom discussions; and encourage students to actively reflect on their intuitions. Future studies should consider the processes governing the development of intuition and expand research on students' epistemological views on intuition.

There is a need for expanding research on upper-division physics courses, in particular topics such as thermal physics. Our study took a grounded approach to exploring challenges that arose when small student groups engaged in collaborative problem solving on statistical mechanics content. We found that the students struggled to navigate around the abstract and subtle concepts of statistical mechanics. Additionally, challenges related to problem-solving strategies was prevalent in our data. Here we will summarize our identified categories of student challenges, which emerged from our data, and present a few illustrative examples. Particularly, we will discuss the educational implications of our findings and the possible connections to other upper-division courses with a similar reliance on abstract physics concepts and demanding mathematics.

Intuition has been reported as being pivotal in guiding students' problem solving. In this ongoing project, we employ a grounded approach to investigate how students use intuition during problem solving in beyond-intro chemistry and physics courses. We adopt a dynamic perspective on intuition, recognizing its context-dependency, to examine how students respond to their intuitions. In a case study, we inductively analyze existing video data of problem-solving sessions, and show that students' responses to intuition can be productive or unproductive, regardless of the intuition's appropriateness. This highlights the need to equip students with strategies to manage their intuitions productively. Based on our findings, we recommend teachers to: adopt a flexible stance toward intuition; explicitly incorporate the topic of intuition in classroom discussions; and encourage students to actively reflect on their intuitions. Future studies should consider the processes governing the development of intuition and expand research on students' epistemological views on intuition.

The two-state paramagnet has previously been proposed as a valuable pedagogical tool for teaching statistical mechanics. In this study, we focused on the role that the two-state paramagnet example played in student discussions while solving problems in statistical mechanics. Students' use of the example was both advantageous and challenging. While we saw students using the two-state paramagnet example to reason analogically about similar systems, we also saw a general lack of in-depth reflection of what makes the model transferable to other contexts. We suggest some considerations for teachers to better leverage this example and facilitate student learning in statistical mechanics.

Problem solving at the interface of mathematics and other scientific disciplines is known to pose substantial challenges for students at the university level. In our research, we employ lenses from physics, chemistry, and mathematics education research, to explore students' approaches to math-intensive problem solving beyond introductory level physics and chemistry. Preliminary findings indicate that effective problem-solving activities in these contexts require students to combine their understanding of concepts and problem-solving skills from both mathematics and chemistry or physics. Interestingly, this includes their intuition or 'gut feelings' related to these disciplines. At TUK2024, we will present illustrative examples that emerged from our empirical data, highlighting the influence of students' intuition on how they navigate uncertain problem-solving situations. While our findings originated within the realms of chemistry and physics, we believe that their implications for teaching extend to, and are relevant to, students' problem-solving tendencies in other scientific disciplines.

This case study aimed to investigate patterns in student reasoning in statistical mechanics, a rather unrepresented topic in Physics Education Research. We recorded problem-solving groups of upper-division physics students at Uppsala University. The initial qualitative analysis of the data revealed previously reported student difficulties and other common themes. We found an unproductive intuition, or "gut feeling", in all groups when reasoning about the high temperature limit of a discrete system in contact with a heat bath. Interestingly, our findings suggest that the students then productively used analogical reasoning to solve the problem. The students improved their reasoning by considering a typical example from quantum mechanics involving spin, transferring knowledge from one physics domain to another physics domain. Our findings can inform teachers and encourage them to help students use productive ideas. Future work includes identifying more productive ideas of various kinds and studying students' beliefs about problem-solving in statistical mechanics.

This exploratory case study aimed to investigate patterns in student reasoning in statistical mechanics, in order to identify difficulties and develop ideas for future research. Upper-division undergraduate students, taking a course in statistical mechanics, were interviewed in groups. Here we present observed patterns of student reasoning about a simple, discrete system in contact with a heat bath. Our findings reveal problematic student intuitions of the high temperature limit. Several students were, however, able to transfer knowledge from a similar problem involving spin to improve their reasoning.

Proteins often carry an intrinsic electric dipole moment, which can interact with external electric fields and cause protein motion. Previous research has found that the orientation of small proteins in gas phase can be controlled in a static electric field. This effect is hoped to benefit applications such as single-particle imaging, and possibly other techniques involving proteins in electric fields. With the purpose of improving our understanding and modeling of protein orientation, this project investigated the scarcely explored quantum mechanical aspects of the process, namely the polarizability. Ground-state electronic structure simulations of three small model proteins, ubiquitin, Trp-cage and lysozyme, under the influence of electric fields were performed in vacuum. The electric dipole moments of the proteins were extracted from simulations with an applied electric field of strength 1 V/nm for varying angles, with respect to a body fixed reference frame. A Python program was written to analyze and visualize the results. The results point to a connection between the polarizability and the structure of the proteins, as well as size. Next a 3D rigid rotor model was developed using Mathematica in order to study the orientation dynamics classically in a simplified and time efficient way, with the possibility of including the previous quantum results. A comparison between a simulation of ubiquitin with and without polarizability concluded that the polarizability seems to have a damping effect on the orientation dynamics, at least for the initial conditions tested in this study. Further research is necessary to validate the model and perform statistical analysis of many simulations with varying initial conditions., Proteiner bär ofta på ett inneboende elektriskt dipolmoment, som vid interaktion med externa elektriska fält och orsakar rörelse hos proteinerna. Tidigare studier har funnit att orienteringen av små proteiner i gasfas kan kontrolleras i ett statiskt elektriskt fält. Den effekten kan förhoppningsvis vara en fördel i tillämpningar såsom single-particle imaging, och eventuellt andra tekniker som innefattar proteiner i elektriska fält. I syftet att förbättra vår förståelse och modellering av protein-orientering, har detta projekt undersökt de föga utforskade kvantmekaniska aspekterna av processen, nämligen polariserbarheten. Kvant-baserade simuleringar av grundtillståndet av tre små proteiner, ubiquitin, Trp-cage och lysozym, under påverkan av elektriska fält utfördes i vakuum. Proteinernas elektriska dipolmoment extraherades från simuleringar med ett elektriskt fält med styrkan 1 V/nm för olika vinklar, med avseende på ett kroppsfixerat koordinatsystem. Ett Python-program skrevs för att analysera och visualisera resultaten. Resultaten tyder på att polariserbarheten beror på strukturen och storleken av proteinerna. Därefter utformades en stel-rotor-modell med hjälp av Mathematica för att studera prienteringen klassiskt på ett förenklat och tidseffektivt sätt, med möjligheten att inkludera de tidigare kvantmekaniska resultaten. En jämförelse mellan en simulering av ubiquitin med och utan polariserbarhet konstaterade att polariserbarheten verkar ha en dämpande effekt på orienteringen, åtminstone för begynnelsevillkoren som testades i denna studie. Vidare forskning krävs för att styrka modellen och utföra statistisk analys av många simuleringar med varierande begynnelsevillkor.

We demonstrate site-specific X-ray induced fragmentation across the sulfur L-edge of protonated cystine, the dimer of the amino acid cysteine. Ion yield NEXAFS were performed in the gas phase using electrospray ionization (ESI) in combination with an ion trap. The interpretation of the sulfur Ledge NEXAFS spectrum is supported by Restricted Open-Shell Configuration Interaction (ROCIS) calculations. The fragmentation pathway of triply charged cystine ions was modeled by Molecular Dynamics (MD) simulations. We have deduced a possible pathway of fragmentation upon excitation and ionization of S 2p electrons. The disulfide bridge breaks for resonant excitation at lower photon energies but remains intact upon higher energy resonant excitation and upon ionization of S 2p. The larger fragments initially formed subsequently break into smaller fragments.