Urban infrastructures and services—such as public transportation, innovation bodies and environmental services—are important drivers for the sustainable development of our society. How effectively citizens, institutions and enterprises interact, how quickly technological innovations are implemented and how carefully new policies are pursued, synergically determine development. In this work, data related to urban infrastructure features such as patents and recycled waste referred to 106 province areas in Italy are investigated over a period of twenty years (2001–2020). Scaling laws with exponents characterizing the above mentioned features are observed and adopted to scrutinize whether and how multiple interactions within a population have amplification effects on the recycling and innovation performance. The study shows that there is a multiplication effect of the population size on the innovation performance of territories, meaning that the dynamic interactions among the elements of the innovation eco-systems in a territory increase its innovation performance. We discuss how to use such approach and the related indexes for understanding metropolitan development policy.

1. Adams, R., Jeanrenaud, S., Bessant, J., et al. (2016). Sustainability-oriented Innovation: A Systematic Review. International Journal of Management Reviews, 18(2), 180–205. https://doi.org/10.1111/ijmr.12068
2. Alcamo, L., Carbone, A., Manzini, R., et al. (2024). Innovation and Waste Disposal Italian Metropolitan Areas. Mendeley Data V1. doi: 10.17632/bv6nxvfxcz.1
3. Aldieri, L., Ioppolo, G., Vinci, C. P., et al. (2019). Waste recycling patents and environmental innovations: An economic analysis of policy instruments in the USA, Japan and Europe. Waste Management, 95, 612–619. https://doi.org/10.1016/j.wasman.2019.06.045
4. Audretsch, D. B., & Feldman, M. P. (2004). Knowledge spillovers and the geography of innovation. In: Handbook of regional and urban economics. Elsevier. pp. 2713–2739.
5. Barr, S. (2007). Factors influencing environmental attitudes and behaviors: A UK case study of household waste management. Environment and Behavior, 39(4), 435–473. https://doi.org/10.1177/0013916505283421
6. Bettencourt, L. M. A., & Lobo, J. (2016). Urban scaling in Europe. Journal of The Royal Society Interface, 13(116), 20160005. https://doi.org/10.1098/rsif.2016.0005
7. Bettencourt, L. M. A., Lobo, J., Helbing, D., et al. (2008). Growth, innovation, scaling, and the pace of life in cities. Proceedings of the National Academy of Sciences, 104(17), 7301–7306. https://doi.org/10.1073/pnas.0610172104
8. Bettencourt, L. M. A., Lobo, J., & Strumsky, D. (2007). Invention in the city: Increasing returns to patenting as a scaling function of metropolitan size. Research Policy, 36(1), 107–120. https://doi.org/10.1016/j.respol.2006.09.026
9. Bettencourt, L., & West, G. (2010). A unified theory of urban living. Nature, 467(7318), 912–913. https://doi.org/10.1038/467912a
10. Bonino, D., Ciaramella, A., & Corno, F. (2010). Review of the state-of-the-art in patent information and forthcoming evolutions in intelligent patent informatics. World Patent Information, 32(1), 30–38. https://doi.org/10.1016/j.wpi.2009.05.008
11. Burghardt, K., Uhl, J. H., Lerman, K., et al. (2024). Analyzing urban scaling laws in the United States over 115 years. Environment and Planning B: Urban Analytics and City Science. https://doi.org/10.1177/23998083241240099
12. Carbone, A., da Silva, S., & Kaniadakis, G. (2024). Capturing urban scaling laws via spatio-temporal correlated clusters. In: Urban Scaling: Allometry in Urban Studies and Spatial Science. pp: 318-331 Routledge. Taylor & Francis https://doi.org/10.4324/9781003288312-36
13. Carbone, A., Murialdo, P., Pieroni, A., et al. (2022). Atlas of urban scaling laws. Journal of Physics: Complexity, 3(2), 025007. https://doi.org/10.1088/2632-072x/ac718e
14. Cheng, L., Mi, Z., Sudmant, A., et al. (2022). Bigger cities better climate? Results from an analysis of urban areas in China. Energy Economics, 107, 105872. https://doi.org/10.1016/j.eneco.2022.105872
15. Fleming, L. (2001). Recombinant Uncertainty in Technological Search. Management Science, 47(1), 117–132. https://doi.org/10.1287/mnsc.47.1.117.10671
16. Furman, J. L., Porter, M. E., & Stern, S. (2002). The determinants of national innovative capacity. Research policy, 31(6), 899–933.
17. Gambardella, A. (1994). The changing technology of technical change: General and abstract knowledge and the division of innovative labor. Research Policy, 23, 523–532.
18. J. Acs, Z., & Audretsch, D. B. (1989). Patents as a Measure of Innovative Activity. Kyklos, 42(2), 171–180. https://doi.org/10.1111/j.1467-6435.1989.tb00186.x
19. Jacobs, J. (1985). Cities and the wealth of nations: Principles of economic life. Vintage.
20. Jaffe, A. B., Trajtenberg, M., & Henderson, R. (1993). Geographic Localization of Knowledge Spillovers as Evidenced by Patent Citations. The Quarterly Journal of Economics, 108(3), 577–598. https://doi.org/10.2307/2118401
21. Jesson, J., Pocock, R., & Stone, I. (2014). Barriers to recycling: A review of evidence since 2008. The Waste & Resources Action Programme: Banbury, UK.
22. Keuschnigg, M., Mutgan, S., & Hedström, P. (2019). Urban scaling and the regional divide. Science Advances, 5(1). https://doi.org/10.1126/sciadv.aav0042
23. Kirchherr, J., Reike, D., & Hekkert, M. (2017). Conceptualizing the circular economy: An analysis of 114 definitions. Resources, Conservation and Recycling, 127, 221–232. https://doi.org/10.1016/j.resconrec.2017.09.005
24. Knickmeyer, D. (2020). Social factors influencing household waste separation: A literature review on good practices to improve the recycling performance of urban areas. Journal of Cleaner Production, 245, 118605. https://doi.org/10.1016/j.jclepro.2019.118605
25. Köhler, J., Geels, F. W., Kern, F., et al. (2019). An agenda for sustainability transitions research: State of the art and future directions. Environmental Innovation and Societal Transitions, 31, 1–32. https://doi.org/10.1016/j.eist.2019.01.004
26. Liu, Z., Schraven, D., de Jong, M., et al. (2023). Unlocking system transitions for municipal solid waste infrastructure: A model for mapping interdependencies in a local context. Resources, Conservation and Recycling, 198, 107180. https://doi.org/10.1016/j.resconrec.2023.107180
27. Marseguerra, G., Bragoli, D., & Cortelezzi, F. (2016). Assessing the innovative performance of Italian SMEs. Istituto Lombardo-Accademia di Scienze e Lettere Rendiconti di Lettere.
28. Mayona, E. L., & Sutriadi, R. (2024). Ecological city concept: Challenge and future research agenda in urban ecology perspective. Journal of Infrastructure, Policy and Development, 8(5), 2852. https://doi.org/10.24294/jipd.v8i5.2852
29. Miafodzyeva, S., & Brandt, N. (2013). Recycling Behaviour Among Householders: Synthesizing Determinants Via a Meta-analysis. Waste and Biomass Valorization, 4(2), 221–235. https://doi.org/10.1007/s12649-012-9144-4
30. Narin, F., Carpenter, M. P., & Woolf, P. (1984). Technological performance assessments based on patents and patent citations. IEEE Transactions on Engineering Management, EM-31(4), 172–183. https://doi.org/10.1109/tem.1984.6447534
31. Nordbeck, S. (1971). Urban Allometric Growth. Geografiska Annaler: Series B, Human Geography, 53(1), 54–67. https://doi.org/10.1080/04353684.1971.11879355
32. Pavitt, K. (1985). Patent statistics as indicators of innovative activities: Possibilities and problems. Scientometrics, 7(1–2), 77–99. https://doi.org/10.1007/bf02020142
33. Platon, V., Pavelescu, F. M., Antonescu, D., et al. (2022). Innovation and Recycling—Drivers of Circular Economy in EU. Frontiers in Environmental Science, 10. https://doi.org/10.3389/fenvs.2022.902651
34. Ponta, L., Puliga, G., & Manzini, R. (2021). A measure of innovation performance: the Innovation Patent Index. Management Decision, 59(13), 73–98. https://doi.org/10.1108/md-05-2020-0545
35. Ponta, L., Puliga, G., Oneto, L., et al. (2020). Identifying the Determinants of Innovation Capability with Machine Learning and Patents. IEEE Transactions on Engineering Management, 69(5), 2144–2154. https://doi.org/10.1109/tem.2020.3004237
36. Ribeiro, F. L., & Rybski, D. (2023). Mathematical models to explain the origin of urban scaling laws. Physics Reports, 1012, 1–39. https://doi.org/10.1016/j.physrep.2023.02.002
37. Rybski, D., Arcaute, E., & Batty, M. (2019). Urban scaling laws. Environment and Planning B: Urban Analytics and City Science, 46(9), 1605–1610. https://doi.org/10.1177/2399808319886125
38. Samaniego, H., & Moses, M. E. (2008). Cities as Organisms: Allometric Scaling of Urban Road Networks. Journal of Transport and Land Use, 1(1). https://doi.org/10.5198/jtlu.v1i1.29
39. Stanley, H. E. (1999). Scaling, universality, and renormalization: Three pillars of modern critical phenomena. Reviews of Modern Physics, 71(2), S358–S366. https://doi.org/10.1103/revmodphys.71.s358
40. Sumrin, S., Gupta, S., Asaad, Y., et al. (2021). Eco-innovation for environment and waste prevention. Journal of Business Research, 122, 627–639. https://doi.org/10.1016/j.jbusres.2020.08.001
41. Svennevik, E. M. C. (2022). Practices in transitions: Review, reflections, and research directions for a Practice Innovation System PIS approach. Environmental Innovation and Societal Transitions, 44, 163–184. https://doi.org/10.1016/j.eist.2022.06.006
42. Thomas, C., & Sharp, V. (2013). Understanding the normalisation of recycling behaviour and its implications for other pro-environmental behaviours: A review of social norms and recycling. Resources, Conservation and Recycling, 79, 11–20. https://doi.org/10.1016/j.resconrec.2013.04.010
43. Van Mierlo, B., & Beers, P. J. (2020). Understanding and governing learning in sustainability transitions: A review. Environmental Innovation and Societal Transitions, 34, 255–269. https://doi.org/10.1016/j.eist.2018.08.002
44. Vanderlei, C. A., Kniess, C., & Quoniam, L. (2020). Patent technometry by mind maps: a study on the recycling of waste electrical and electronic equipment. International Journal of Innovation, 8(1), 77–100. https://doi.org/10.5585/iji.v8i1.16480
45. Zisopoulos, F. K., Schraven, D. F. J., & de Jong, M. (2022). How robust is the circular economy in Europe? An ascendency analysis with Eurostat data between 2010 and 2018. Resources, Conservation and Recycling, 178, 106032. https://doi.org/10.1016/j.resconrec.2021.106032