Resource-Bounded Distinction Systems

Appendix C: Literature References

Foundations.

  • Karoubi, M. (1978). K-theory: An introduction. Springer.
  • Mac Lane, S. (1971). Categories for the working mathematician. Springer.
  • Lawvere, F. W. (1964). An elementary theory of the category of sets. PNAS.
  • Lurie, J. (2009). Higher topos theory. Princeton.

Resource theories / graded categories.

  • Coecke, B., Fritz, T., & Spekkens, R. W. (2016). A mathematical theory of resources. Information and Computation, 250, 59-86. arXiv:1409.5531.
  • Chitambar, E., & Gour, G. (2019). Quantum resource theories. Rev. Mod. Phys., 91, 025001. arXiv:1806.06107.
  • Lawvere, F. W. (1973). Metric spaces, generalized logic, and closed categories. Rend. Sem. Mat. Fis. Milano, 43, 135-166.
  • Fujii, S., Katsumata, S., & Melliès, P.-A. (2016). Towards a formal theory of graded monads. FOSSACS 2016, LNCS 9634, 513-530.

Coalgebra and behavioural equivalence.

  • Rutten, J. J. M. M. (2000). Universal coalgebra: A theory of systems. Theoretical Computer Science, 249(1), 3-80.
  • Baldan, P., Bonchi, F., Kerstan, H., & König, B. (2018). Coalgebraic behavioral metrics. Logical Methods in Computer Science, 14(3), 20. arXiv:1712.07511.
  • Hughes, J., & Jacobs, B. (2003). Simulations in coalgebra. Electron. Notes Theor. Comput. Sci., 82(1), 84-99.
  • Hasuo, I. (2006). Generic forward and backward simulations. CONCUR 2006, LNCS 4137, 406-420.

Tolerance relations.

  • Zeeman, E. C. (1962). The topology of the brain and visual perception.
  • Peters, J. F. (2014). Topology of digital images. Springer.

Hybrid systems.

  • Filippov, A. F. (1988). Differential equations with discontinuous righthand sides. Kluwer.
  • Utkin, V. I. (1992). Sliding modes in control and optimization. Springer.

Active matter / Non-reciprocal forces.

  • Ivlev, A. V., Bartnick, J., Heinen, M., Du, C.-R., Nosenko, V., & Löwen, H. (2015). Statistical mechanics where Newton's third law is broken. Phys. Rev. X, 5, 011035. arXiv:1403.2417.
  • Fruchart, M., Hanai, R., Littlewood, P. B., & Vitelli, V. (2021). Non-reciprocal phase transitions. Nature, 592(7854), 363-369. arXiv:2003.13176.
  • Bowick, M. J., Fakhri, N., Marchetti, M. C., & Ramaswamy, S. (2022). Symmetry, thermodynamics and topology in active matter. Phys. Rev. X, 12, 010501. arXiv:2107.00724.
  • Alston, H., Cocconi, L., & Bertrand, T. (2023). Active bound states arise from transiently nonreciprocal pair interactions. Phys. Rev. Research, 5, 043032. arXiv:2304.07738.
  • Scheibner, C., Souslov, A., Banerjee, D., Surówka, P., Irvine, W. T. M., & Vitelli, V. (2020). Odd elasticity. Nature Physics, 16, 475-481. arXiv:1902.07760.
  • Tan, T. H., et al. (2022). Odd dynamics of living chiral crystals. Nature, 607, 287-293.
  • Chao, Y.-C., Gokhale, S., Lin, L., Hastewell, A., Bacanu, A., Chen, Y., Li, J., Liu, J., Lee, H., Dunkel, J., & Fakhri, N. (2026). Selective excitation of work-generating cycles in non-reciprocal living solids. Nature Physics. arXiv:2410.18017.
  • "Topological flowscape reveals state transitions in nonreciprocal living matter." Phys. Rev. X (accepted). arXiv:2511.11815.
  • Ballerini, M., et al. (2008). Interaction ruling animal collective behavior depends on topological rather than metric distance. PNAS, 105, 1232.
  • Dechant, A., Sasa, S.-i., & Ito, S. (2022). Geometric decomposition of entropy production into excess, housekeeping, and coupling parts. Phys. Rev. E, 106, 024125. arXiv:2202.04331.

Transformers / attention as particle systems.

  • Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., & Polosukhin, I. (2017). Attention is all you need. Advances in Neural Information Processing Systems, 30, 5998-6008. arXiv:1706.03762.
  • Rauh, J., Banerjee, A., Olbrich, E., Jost, J., Bertschinger, N., & Wolpert, D. H. (2017). Coarse-graining and the Blackwell order. Entropy, 19(10), 527. arXiv:1701.07602. (Garbling orders experiments by informativeness.)
  • Maćkowiak, B., Matějka, F., & Wiederholt, M. (2023). Rational inattention: A review. Journal of Economic Literature, 61(1), 226-273. (Limited information processing and selective attention.)
  • Sander, M. E., Ablin, P., Blondel, M., & Peyré, G. (2022). Sinkformers: Transformers with doubly stochastic attention. Proceedings of Machine Learning Research, 151, 5312-5328. (Doubly-stochastic attention as an established architectural construction.)
  • Geshkovski, B., Letrouit, C., Polyanskiy, Y., & Rigollet, P. (2025). A mathematical perspective on Transformers. Bulletin of the American Mathematical Society, 62(3), 427-479. arXiv:2312.10794.
  • Castin, V., Ablin, P., Carrillo, J. A., & Peyré, G. (2025). A unified perspective on the dynamics of deep Transformers. arXiv:2501.18322.
  • Duerinckx, M., Geshkovski, B., & Rossi, S. (2026). Kinetic theory for Transformers and the lost-in-the-middle phenomenon. arXiv:2605.09213.

Perception-mediated active matter.

  • Loos, S. A. M., Klapp, S. H. L., & Martynec, T. (2023). Long-range order and directional defect propagation in the nonreciprocal XY model with vision cone interactions. Physical Review Letters, 130, 198301. (Configuration-dependent vision cones generate directed interactions.)
  • Durve, M., Saha, S., & Sayeed, A. (2017). Active particle condensation by nonreciprocal and time-delayed interactions. arXiv:1703.09596. (Vision-cone perception as a route to effective non-reciprocity.)

TDA / Persistent homology.

  • Edelsbrunner, H. & Harer, J. L. (2010). Computational topology: An introduction. AMS.
  • Carlsson, G. (2009). Topology and data. Bull. AMS, 46(2), 255-308.

RG / QFT.

  • Wilson, K. G. (1975). The renormalization group. Rev. Mod. Phys., 47(4), 773.

Type theory.

  • Martin-Löf, P. (1984). Intuitionistic type theory. Bibliopolis.

Measure theory.

  • Bogachev, V. I. (2007). Measure theory. Springer.

Operational theories / Reconstruction.

  • Chiribella, G., D'Ariano, G. M., & Perinotti, P. (2010). Probabilistic theories with purification. Phys. Rev. A, 81, 062348.
  • Chiribella, G., D'Ariano, G. M., & Perinotti, P. (2011). Informational derivation of quantum theory. Phys. Rev. A, 84, 012311.
  • Hardy, L. (2011). Reformulating and reconstructing quantum theory. arXiv:1104.2066.
  • Hardy, L. (2013). Reconstructing quantum theory. arXiv:1303.1538.

Quantum Darwinism.

  • Zurek, W. H. (2009). Quantum Darwinism. Nature Physics, 5, 181-188. arXiv:0903.5082.
  • Zurek, W. H. (2022). Quantum theory of the classical. arXiv:2208.09019.

Algorithmic information theory.

  • Li, M., & Vitányi, P. (2008). An introduction to Kolmogorov complexity and its applications (3rd ed.). Springer.
  • Bennett, C. H., Gács, P., Li, M., Vitányi, P., & Zurek, W. H. (1998). Information distance. IEEE Trans. Inf. Theory, 44(4), 1407-1424.

Descriptive complexity / FMT.

  • Immerman, N. (1999). Descriptive complexity. Springer.
  • Ehrenfeucht, A. (1961). An application of games to the completeness problem. Fund. Math., 49, 129-141.

Information geometry.

  • Amari, S. (2016). Information geometry and its applications. Springer.

Observability theory.

  • Kalman, R. E. (1960). On the general theory of control systems. IRE Trans. Automatic Control, 4(3), 110.
  • Hautus, M. L. J. (1969). Controllability and observability conditions. Indag. Math., 31, 443-448.

Sheaf-theoretic contextuality.

  • Abramsky, S., & Brandenburger, A. (2011). The sheaf-theoretic structure of non-locality and contextuality. New J. Phys., 13, 113036.

Quantum reference frames.

  • Bartlett, S. D., Rudolph, T., & Spekkens, R. W. (2007). Reference frames, superselection rules, and quantum information. Rev. Mod. Phys., 79, 555.
  • Castro-Ruiz, E., et al. (2020). Changing quantum reference frames. arXiv:2012.15769.

Optimal transport / Wasserstein.

  • Villani, C. (2009). Optimal transport: Old and new. Springer.
  • Santambrogio, F. (2015). Optimal transport for applied mathematicians. Birkhäuser.

Rényi divergences.

  • van Erven, T., & Harremoës, P. (2014). Rényi divergence and Kullback-Leibler divergence. IEEE Trans. Inf. Theory, 60(7), 3797-3820.
  • Wilde, M. M. (2013). Quantum information theory. Cambridge.
  • Tomamichel, M. (2015). Quantum information processing with finite resources. Springer.

Operator theory / Self-adjointness / Open quantum systems.

  • Reed, M., & Simon, B. (1972-1979). Methods of modern mathematical physics (Vols. I-IV). Academic Press.
  • Connes, A. (1994). Noncommutative geometry. Academic Press.
  • Engel, K.-J., & Nagel, R. (2000). One-parameter semigroups for linear evolution equations. Springer.
  • Breuer, H.-P., & Petruccione, F. (2002). The theory of open quantum systems. Oxford.
  • Lindblad, G. (1976). On the generators of quantum dynamical semigroups. Commun. Math. Phys., 48(2), 119-130.