Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Here we address these questions by studying how compatibility with thermodynamics constrains the structure of quantum theory. We employ two postulates that any probabilistic theory with reasonable thermodynamic behaviour should arguably satisfy. In the framework of generalised probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechanics. Using a thought experiment by von Neumann, we show that these theories admit a consistent thermodynamic notion of entropy, and prove that the second law holds for projective measurements and mixing procedures. Furthermore, we study additional entropy-like quantities based on measurement probabilities and convex decomposition probabilities, and uncover a relation between one of these quantities and Sorkin's notion of higher-order interference.information processing, and in this way to gain a deeper understanding of its characteristic properties in terms of computation or communication.In a complementary approach, there has been a wave of attempts to find simple physical principles that single out quantum correlations from the set of all non-signalling correlations in the device-independent formalism [70]. These include non-trivial communication complexity [71], macroscopic locality [72], or information causality [73]. However, none of these principles so far turns out to yield the set of quantum correlations exactly. This led to the discovery of 'almost quantum correlations ' [75] which are more general than those allowed by quantum theory, but satisfy all the aforementioned principles. Almost quantum correlations seem to appear naturally in the context of quantum gravity [77].A relation to other fields of physics can also be drawn from information causality, which can be understood as the requirement that a notion of entropy [66-69] exists which has some natural properties like the dataprocessing inequality [74]. These emergent connections to entropy and quantum gravity are particularly interesting since they point to an area of physics where modifications of quantum theory are well-motivated: Jacobson's results [78] and holographic duality [79] relate thermodynamics, entanglement, and (quantum) gravity, and modifying quantum theory has been discussed as a means to overcome apparent paradoxes in blackhole physics [80].While GPTs provide a way to generalise quantum theory and to study more general correlations and physical theories, they still leave open the question as to which principles should guide us in applying the GPT formalism for this purpose. The considerations above suggest taking, as a guideline for such modifi...

In a quantum world, reference frames are ultimately quantum systems too – but what does it mean to "jump into the perspective of a quantum particle"? In this work, we show that quantum reference frame (QRF) transformations appear naturally as symmetries of simple physical systems. This allows us to rederive and generalize known QRF transformations within an alternative, operationally transparent framework, and to shed new light on their structure and interpretation. We give an explicit description of the observables that are measurable by agents constrained by such quantum symmetries, and apply our results to a puzzle known as the `paradox of the third particle'. We argue that it can be reduced to the question of how to relationally embed fewer into more particles, and give a thorough physical and algebraic analysis of this question. This leads us to a generalization of the partial trace (`relational trace') which arguably resolves the paradox, and it uncovers important structures of constraint quantization within a simple quantum information setting, such as relational observables which are key in this resolution. While we restrict our attention to finite Abelian groups for transparency and mathematical rigor, the intuitive physical appeal of our results makes us expect that they remain valid in more general situations.