{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T23:50:59Z","timestamp":1773273059927,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,9,1]],"date-time":"2017-09-01T00:00:00Z","timestamp":1504224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011730","name":"Templeton World Charity Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100011730","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NASA Arizona Space Grant"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A major conceptual step forward in understanding the logical architecture of living systems was advanced by von Neumann with his universal constructor, a physical device capable of self-reproduction. A necessary condition for a universal constructor to exist is that the laws of physics permit physical universality, such that any transformation (consistent with the laws of physics and availability of resources) can be caused to occur. While physical universality has been demonstrated in simple cellular automata models, so far these have not displayed a requisite feature of life\u2014namely open-ended evolution\u2014the explanation of which was also a prime motivator in von Neumann\u2019s formulation of a universal constructor. Current examples of physical universality rely on reversible dynamical laws, whereas it is well-known that living processes are dissipative. Here we show that physical universality and open-ended dynamics should both be possible in irreversible dynamical systems if one entertains the possibility of state-dependent laws. We demonstrate with simple toy models how the accessibility of state space can yield open-ended trajectories, defined as trajectories that do not repeat within the expected Poincar\u00e9 recurrence time and are not reproducible by an isolated system. We discuss implications for physical universality, or an approximation to it, as a foundational framework for developing a physics for life.<\/jats:p>","DOI":"10.3390\/e19090461","type":"journal-article","created":{"date-parts":[[2017,9,1]],"date-time":"2017-09-01T11:05:24Z","timestamp":1504263924000},"page":"461","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Physical Universality, State-Dependent Dynamical Laws and Open-Ended Novelty"],"prefix":"10.3390","volume":"19","author":[{"given":"Alyssa","family":"Adams","sequence":"first","affiliation":[{"name":"Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, AZ 85287, USA"},{"name":"Department of Physics, Arizona State University, Tempe, AZ 85287, USA"},{"name":"Algorithmic Nature Group, Laboratoire de Recherche Scientifique (LABORES) for the Natural and Digital Sciences, 75006 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angelica","family":"Berner","sequence":"additional","affiliation":[{"name":"Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, AZ 85287, USA"},{"name":"Department of Physics, Arizona State University, Tempe, AZ 85287, USA"},{"name":"School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul","family":"Davies","sequence":"additional","affiliation":[{"name":"Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, AZ 85287, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5779-2772","authenticated-orcid":false,"given":"Sara","family":"Walker","sequence":"additional","affiliation":[{"name":"Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, AZ 85287, USA"},{"name":"School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA"},{"name":"ASU-SFI Center for Biosocial Complex Systems, Arizona State University, Tempe, AZ 85287, USA"},{"name":"Blue Marble Space Institute of Science, Seattle, WA 98154, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,1]]},"reference":[{"key":"ref_1","unstructured":"Schr\u00f6dinger, E. (1944). What Is Life?, Cambridge University Press."},{"key":"ref_2","unstructured":"Von Neumann, J. (1966). Theory of Self-Reproducing Automata, University of Illinois Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1098\/rsif.2016.1033","article-title":"Semantic Closure Demonstrated by the Evolution of a Universal Constructor Architecture in an Artificial Chemistry","volume":"14","author":"Clark","year":"2017","journal-title":"J. R. Soc. Interface"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1023\/B:ORIG.0000016440.53346.dc","article-title":"A universal definition of life: Autonomy and open-ended evolution","volume":"34","author":"Moreno","year":"2004","journal-title":"Orig. Life Evol. Biosph."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"20141226","DOI":"10.1098\/rsif.2014.1226","article-title":"Constructor Theory of Life","volume":"12","author":"Marletto","year":"2015","journal-title":"J. R. Soc. Interface"},{"key":"ref_6","unstructured":"Deutsch, D. (2011). The Beginning of Infinitiy: Explanations that Transform the World, Penguin."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4331","DOI":"10.1007\/s11229-013-0279-z","article-title":"Constructor Theory","volume":"190","author":"Deutsch","year":"2013","journal-title":"Synthese"},{"key":"ref_8","unstructured":"Janzing, D. (2010). Is There a Physically Universal Cellular Automaton or Hamiltonian?. arXiv."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Schaeffer, L. (, January 11\u201313). A Physically Universal Celllular Automaton. Proceedings of the 2015 Conferences on Innovations in Theoretical Computer Science, Rehovot, Israel.","DOI":"10.1145\/2688073.2688107"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Salo, V., and T\u00f6rm\u00e4, I. (2017, January 12\u201316). A One-Dimensional Physically Universal Cellular Automaton. Proceedings of the Conference on Computability in Europe, Turku, Finland.","DOI":"10.1007\/978-3-319-58741-7_35"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Schaeffer, L. (2015, January 8\u201310). A Physically Universal Cellular Automaton. Proceedings of the International Workshop on Cellular Automata and Discrete Complex Systems, Turku, Finland.","DOI":"10.1007\/978-3-662-47221-7_4"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1038\/s41598-017-00810-8","article-title":"Formal Definitions of Unbounded Evolution and Innovation Reveal Universal Mechanisms for Open-Ended Evolution in Dynamical Systems","volume":"7","author":"Adams","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_13","unstructured":"Pavlic, T.P., Adams, A.M., and Walker, S.I. (August, January 30). Self-referencing Cellular Automata: A Model of the Evolution of Information Control in Biological Systems. Proceedings of the Fourteenth International Conference on the Synthesis and Simulation of Living Systems, New York, NY, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"026203","DOI":"10.1103\/PhysRevE.73.026203","article-title":"Coarse-graining of cellular automata, emergence, and the predictability of complex systems","volume":"73","author":"Israeli","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_15","unstructured":"Hooft, G. (2014). The Cellular Automaton Interpretation of Quantum Mechanics. arXiv."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0167-2789(84)90254-9","article-title":"Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics","volume":"10","author":"Toffoli","year":"1984","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0167-2789(90)90064-V","article-title":"Computation at the edge of chaos: Phase transitions and emergent computation","volume":"42","author":"Langton","year":"1990","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0167-2789(94)90273-9","article-title":"The calculi of emergence: Computation, dynamics and induction","volume":"75","author":"Crutchfield","year":"1994","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_19","unstructured":"Borriello, E., and Walker, S.I. (2016). An Information-Theoretic Classification of Complex Systems. arXiv."},{"key":"ref_20","unstructured":"Wolfram, S. (2002). A New Kind of Science, Wolfram Media."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0167-2789(84)90252-5","article-title":"Physics-Like Models of Computation","volume":"10","author":"Margolus","year":"1984","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_22","first-page":"4","article-title":"The Game of Life","volume":"223","author":"Conway","year":"1970","journal-title":"Sci. Am."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.25088\/ComplexSystems.15.1.1","article-title":"Universality in Elementary Cellular Automata","volume":"15","author":"Cook","year":"2004","journal-title":"Complex Syst."},{"key":"ref_24","unstructured":"Nobili, R., and Pesavento, U. (1994). John von Neumann\u2019s automata revisited. Artificial Worlds and Urban Studies, Istituto Universitario di Architettura."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Walker, S.I. (2016). The Descent of Math. Trick or Truth?, Springer International Publishing.","DOI":"10.1007\/978-3-319-27495-9_16"},{"key":"ref_26","first-page":"685","article-title":"The Converse of Moore\u2019s Garden-of-Eden Theorem","volume":"14","author":"Myhill","year":"1963","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Hoel, E.P. (2017). When the map is better than the territory. Entropy, 19.","DOI":"10.3390\/e19050188"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/S0167-2789(99)00230-4","article-title":"Functional Dynamics: I: Articulation Process","volume":"138","author":"Kataoka","year":"2000","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/S0167-2789(00)00203-7","article-title":"Functional Dynamics: II: Syntactic Structure","volume":"149","author":"Kataoka","year":"2001","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_30","unstructured":"Hofsadter, D. (1979). Godel, Escher, Bach: An Eternal Golden Braid, Basic Books."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"102601","DOI":"10.1088\/0034-4885\/79\/10\/102601","article-title":"The Hidden Simplicity of Biology: A Key Issues Review","volume":"79","author":"Davies","year":"2016","journal-title":"Rep. Prog. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1146\/annurev-conmatphys-062910-140509","article-title":"Life Is Physics: Evolution as a Collective Phenomenon Far from Equilibrium","volume":"2","author":"Goldenfeld","year":"2011","journal-title":"Annu. Rev. Condens. Matter Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"20120869","DOI":"10.1098\/rsif.2012.0869","article-title":"The Algorithmic Origins of Life","volume":"6","author":"Walker","year":"2013","journal-title":"J. R. Soc. Interface"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"11641","DOI":"10.1073\/pnas.1204263109","article-title":"Work and information processing in a solvable model of Maxwell\u2019s demon","volume":"109","author":"Mandal","year":"2012","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"190601","DOI":"10.1103\/PhysRevLett.116.190601","article-title":"Maxwell demon dynamics: Deterministic chaos, the Szilard map, and the intelligence of thermodynamic systems","volume":"116","author":"Boyd","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Friston, K. (2013). Life as We Know It, Royal Society Publishing.","DOI":"10.1098\/rsif.2013.0475"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s12064-016-0229-7","article-title":"Defining and simulating open-ended novelty: Requirements, guidelines, and challenges","volume":"135","author":"Banzhaf","year":"2016","journal-title":"Theory Biosci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1112\/plms\/s2-42.1.230","article-title":"On computable numbers, with an application to the Entscheidungsproblem","volume":"2","author":"Turing","year":"1937","journal-title":"Proc. Lond. Math. Soc."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3206","DOI":"10.1039\/C5MB00593K","article-title":"Prebiotic network evolution: Six key parameters","volume":"11","author":"Nghe","year":"2015","journal-title":"Mol. BioSyst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u2018small-world\u2019 networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Kauffman, S.A. (2000). Investigations, Oxford University Press.","DOI":"10.1093\/oso\/9780195121049.001.0001"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1111\/j.1574-6976.2008.00137.x","article-title":"Bacteria as computers making computers","volume":"33","author":"Danchin","year":"2009","journal-title":"FEMS Microbiol. Rev."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Hickinbotham, S.J., and Stepney, S. (2016). Bio-Reflective Architectures for Evolutionary Innovation. Proceedings of the Artificial Life Conference, MIT Press.","DOI":"10.1162\/978-0-262-33936-0-ch038"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1038\/35036627","article-title":"The large-scale organization of metabolic networks","volume":"407","author":"Jeong","year":"2000","journal-title":"Nature"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"13591","DOI":"10.1073\/pnas.0705396104","article-title":"Innovation and robustness in complex regulatory gene networks","volume":"104","author":"Ciliberti","year":"2007","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_46","unstructured":"Wagner, A. (2014). Arrival of the Fittest: Solving Evolution\u2019s Greatest Puzzle, Penguin."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/9\/461\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:53Z","timestamp":1760208233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/9\/461"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,1]]},"references-count":46,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["e19090461"],"URL":"https:\/\/doi.org\/10.3390\/e19090461","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,1]]}}}