Research

• Classical and quantum Brownian motion in an electromagnetic field
  M. Patriarca and P. Sodano
  Fortschritte der Physik 65 (6-8), 1600058 (2017)
  doi:10.1002/prop.201600058   
  arxiv:1605.04698

• M. Patriarca
  Feynman-Vernon model for a moving thermal environment
  Physica E 29 (2005) 243  
  doi:10.1016/j.physe.2005.05.021
  https://arxiv.org/abs/1803.10300

• B.L. Altschuler, C. Biagini, and M. Patriarca
  Quantum chaos and transport in mesoscopic systems
  in: Field Theories for low dimensional systems, G. Morandi et al. editors,
  Springer Series in Solid-State Sciences, vol 131, Springer, Berlin (2000),  p. 235-269
  doi:10.1007/978-3-662-04273-1_7

• M. Patriarca
  Quantum mechanical versus stochastic processes in path integration
  in: Path Integrals from peV to TeV: 50 years after Feynman’s Paper
  R. Casalbuoni et al. editors, World Scientific, Singapore, 1999, p.589
  arxiv:1801.00510

• C. Presilla, R. Onofrio, and M. Patriarca
  Classical and quantum measurements of position
  J. Phys. A 30(21) (1997) 7385  
  doi:10.1088/0305-4470/30/21/014    arXiv:hep-th/9406024

• M. Patriarca
  Statistical correlations in the oscillator model of quantum dissipative systems
  Il Nuovo Cimento B 111 (1996) 61  
  doi:10.1007/BF02726201    arxiv:1801.02429

• F. Illuminati, M. Patriarca, and P. Sodano
  Quantum dissipation in non-homogeneous environments
  in: Fluctuation Phenomena: Disorder and Nonlinearity
  A.R. Bishop, S. Jimenez and L. Vazquez editors, World Scientific, Singapore (1995), p.53.
  doi:10.1142/9789814503877_0012

• F. Illuminati, M. Patriarca, and P. Sodano
  Classical and quantum dissipation in nonhomogeneous environments
  Physica A 211 (1994) 449  
  doi:10.1016/0378-4371(94)00171-5   arXiv:hep-th/9406024

• M. Patriarca
  Boundary conditions for the Schrödinger equation in the simulation of quantum systems
  Phys. Rev. E 50 (1994) 1616 
  doi:10.1103/PhysRevE.50.1616 & Erratum doi:10.1103/b6qb-59f6    

• M. Patriarca
  Sistemi Quantistici in Ambienti Dissipativi, Tesi di Dottorato
  [English translation: Quantum Systems in Dissipative Environments, Phd Thesis]
  University of Perugia (1993) 

• F. A. Gianturco, M. Patriarca, and O. Roncero
  Resonant states and photodissociation cross sections in protonated rare gases
  Molecular Physics 67 (1989) 281  
  doi:10.1080/00268978900101081  

• F. A. Gianturco and M. Patriarca
  Accurate Ne-H+ and Ar-H+ interactions from spectroscopic and scattering states
  Il Nuovo Cimento 11 D (1989) 1287  
  doi:10.1007/BF02450546  

• M. Patriarca
  Ioni Molecolari semplici, Tesi di Laurea
  [English translation: Simple Molecular Ions, Master Thesis]
  La Sapienza University, Rome (1986)

In many ways, linguistics has been an interdisciplinary discipline (with a large overlap with the current complexity science) since its beginning.
The reason is that its subject of study, that is language, has many peculiar features that make it an evolving and adapting systems with different levels of complexity. That is aso the reason why complex systems theory and its tools can be applied effectively to linguistics, both in terms of general concepts and practical applications. 

Language competition, evolution, and spreading processes can be described by different types models that describe the dynamics at different coarse grained levels, from microscopic heterogeneous many-agent models to mesoscopic reaction-diffusion models, from statistical models of word sequence to generative grammars. 

• Learning thresholds lead to stable language coexistence,
  Mikhail V. Tamm, Els Heinsalu, Stefano Scialla, Marco Patriarca,
  https://doi.org/10.1103/PhysRevE.111.024304     arXiv:2406.14522

• Language Dynamics: Complex Systems Approaches,
  Els Heinsalu, Marco Patriarca, David Sanchez,
  in: Reference Collection in Social Sciences,
  International Encyclopedia of Language and Linguistics, 3rd edition, Elsevier 2025
  https://doi.org/10.1016/B978-0-323-95504-1.00991-1  

• Role of zealots in the spread of linguistic traits,
  V. Dornelas, C. Anteneodo, R. Nunes, E. Heinsalu, M. Patriarca,
  Phys. Rev. E 112, 044303
  https://link.aps.org/doi/10.1103/t4pt-zdc3    https://arxiv.org/abs/2508.01500  

• Complexity in Language Variation and Change (Research Topic Editorial)
  Els Heinsalu, Marco Patriarca, and David Sanchez,
  Frontiers in Complex Systems, Vol. 2 (2024)
  doi: 10.3389/fcpxs.2024.1497038 🔓
  The article collection Complexity in Language Variation and Change can be found at:
  https://www.frontiersin.org/research-topics/52099/complexity-in-language-variation-and-change/articles 

• Language dynamics model with finite-range interactions influencing the diffusion of linguistic traits and human dispersal,
  Clément Zankoc, Els Heinsalu, Marco Patriarca,
  European Physical Journal B 97, 66 (2024)
  https://doi.org/10.1140/epjb/s10051-024-00706-3

• A three-state language competition model including language learning and attrition,
  Stefano Scialla, Jens-Kristjan Liivand, Marco Patriarca, Els Heinsalu,
  Front. Complex Syst. 1-1266733 (2023),  
  https://doi.org/10.3389/fcpxs.2023.1266733 🔓

• The Physics of Languages
  Marco Patriarca, Els Heinsalu, and David Sánchez
  Physics World, 13 June 2023
  https://physicsworld.com/a/the-physics-of-languages/

• The role of bilinguals in the Bayesian naming game,
  Gionni Marchetti, Marco Patriarca, Els Heinsalu.
  Physica D 428, 133062 (2021)
  doi:10.1016/j.physd.2021.133062   arXiv:2106.00069

• "Languages in Space and Time: Models and Methods from Complex Systems Theory"
  M. Patriarca, E. Heinsalu, and J.L. Leonard,
  Series Physics of Society: Econophysics and Sociophysics
  Cambridge University Press (2020) ISBN 978-1-108-48065-9

• A Bird’s-Eye View of Naming Game Dynamics: From Trait Competition to Bayesian Inference,
  G. Marchetti, M. Patriarca, and E. Heinsalu,
  Chaos 30, 063119 (2020)  
  doi:10.1063/5.0009569    
  arXiv:2004.01994

• A Bayesian Approach to the Naming Game Model,
  G. Marchetti, M. Patriarca, and E. Heinsalu,
  Frontiers in Physics 8, 10 (2020)  
  doi:10.3389/fphy.2020.00010 🔓    
  arXiv:1911.13012

• Applicazioni alla linguistica dei metodi e modelli della teoria dei sistemi complessi
  M. Patriarca, E. Heinsalu, and J.L. Léonard
  In: "Mutamento Linguistico e Biodiversità", Il Calamo, Roma, 2018, p. 103–143
  Atti del XLI Convegno Società Italiana di Glottologia, Perugia, 1-3 dicembre 2016;
  L. Costamagna et al. editors,  ISBN: 9788898640317,
  Biblioteca della Società Italiana di Glottologia 41 p. 103–143 🔓 

• The role of dispersal in competition success and in the emerging diversity
  E. Heinsalu, D. Navidad Maeso, and M. Patriarca
  The European Physical Journal B  91, 255 (2017)
  https://doi.org/10.1140/epjb/e2018-90372-5  
  arxiv:2004.06088 

• Patterns of Linguistic Diffusion in Space&Time: The Case of Mazatec
  J.-L. Léonard, E. Heinsalu, and M. Patriarca, 
  in: Econophysics and Sociophysics: Recent Progress and Future Directions
  F. Abergel et al. editors, Spriger (2017), p.227-251.
  doi:10.1007/978-3-319-47705-3_17   
  arXiv:1612.02994

• Modeling Regional Variation from EAS: Complexity and Communal Aggregates
  J.L. Léonard, E. Heinsalu, M. Patriarca, and P. Darlu
  Linguistic variation in the basque and education-1 (2015), Servicio Editorial de la Universidad del País Vasco, ISBN: 978-84-9082-278-4, p. 145-172 🔓 

• Variation dialectal del Tseltal Maya (Maya occidental) en los ámbitos morfológico, fonológico y léxico: un enfoque holístico del diasistema
  G. Polian, J.L. Léonard, E. Heinsalu, M. Patriarca
  in: Patterns in Mesoamerican Morphology, J.L. Léonard and A. Kihm editors
  Michel Houdiard Éditeur (2014), p.  280 

• The role of bilinguals in language competition
  E. Heinsalu, M. Patriarca, and J.L. Léonard
  Advances in Complex Systems 17 (01), 1450003 (2014)
  doi:10.1142/S0219525914500039 

• M. Patriarca, X. Castelló, J.R. Uriarte, V.M. Eguı́luz, and M. San Miguel
  Modeling two-language competition dynamics
  Advances in Complex Systems 15 (2012) 1250048  
  doi:10.1142/S0219525912500488  
  arXiv:1206.2960

• M. Patriarca and E. Heinsalu
  Influence of geography on language competition
  Physica A 388 (2009) 174
  doi:10.1016/j.physa.2008.09.034   
  arxiv.org:0807.3100

• M. Patriarca and T. Leppänen
  Modelling language competition
  Physica A 338 (2004) 296  
  doi:10.1016/j.physa.2004.02.056

The full shape of wealth distribution from small to large values of wealth has represented a challenge for economics since the time of the pioneering works of Pareto. The analogy between economic exchanges of wealth between economic agents and energy exchange between e.g. molecules of a fluid was originally suggested by Benoit Mandelbrot in the 60's but has been fully appreciated and worked out only starting at the end of the 90's. There is now a solid research line on the family of models referred to as "kinetic wealth exchange models" that shows how such models can take into account relevant economic sides as saving propensity/productivity, taxation, loans, behavioral traits, etc. to produce wealth distributions in excellent agreement with real data.

On the top of this, wealth-exchange models have provides an ideal framework for testing the general hypothesis of the role of noise and diversity underlying the origin of the observed power law distributions.

• The microscopic origin of the Pareto law and other power-law distributions
  M. Patriarca, E. Heinsalu, A. Chakraborti, and K. Kaski
  in: Econophysics and Sociophysics: Recent Progress and Future Directions
  F. Abergel et al. editors, Springer (2017), p. 159-176.
  doi:10.1007/978-3-319-47705-3_12   

• Kinetic Exchange Models as D Dimensional Systems: A Comparison of Different Approaches
  M. Patriarca, E Heinsalu, A Singh, A Chakraborti
  in: Econophysics and Sociophysics: Recent Progress and Future Directions
  F. Abergel et al. editors, Springer (2017), p 147-158.
  doi:10.1007/978-3-319-47705-3_11 
  Previous version Thermal Equilibrium in D-dimensions: From Fluids and Polymers to Kinetic Wealth Exchange Models arxiv.org:1610.03367

• Power-laws as statistical mixtures
  M. Patriarca, E. Heinsalu, L. Marzola, A. Chakraborti, and K. Kaski
  In: Proceedings of ECCS 2014: European Conference on Complex Systems, 271-282 (2016)
  doi:10.1007/978-3-319-29228-1_23   

• Uni-vs. bi-directional kinetic exchange models
  E. Heinsalu and M. Patriarca
  International Journal of Computational Economics and Econometrics 5 (3), 213-219 (2015)
  doi:10.1140/epjb/e2014-50270-6     
  RePEc:ids:ijcome:v:5:y:2015:i:3:p:213-219

• Kinetic Wealth Exchange Models: A short review
  M. Patriarca and E. Heinsalu
  ICCSA20024 - The 4th International Conference on Complex Systems and Applications, 
  Normandie University, Le Havre, France - June 23-26 (2014)
  Proceedings of ICCSA 2014, p.129-136

• Kinetic models of immediate exchange
  E. Heinsalu and M. Patriarca
  The European Physical Journal B 87, 170 (2014)
  doi:10.1140/epjb/e2014-50270-6    
  arxiv:1505.01274 

• M. Patriarca and A. Chakraborti
  Kinetic exchange models: From molecular physics to social science
  Am. J. Phys. 81, 618 (2013)  
  doi:10.1119/1.4807852  
  arXiv:1305.0768

• A. Chakraborti, I.M. Toke, M. Patriarca, and F. Abergel
  Econophysics review: I. Empirical facts, Quantitative Finance 11 (2011) 991-1012 doi:10.1080/14697688.2010.539248
  Econophysics review: II. Agent-based models, Quantitative Finance 11 (2011) 1013-1041  doi:10.1080/14697688.2010.539249 arXiv:0909.1974

• M. Patriarca, E. Heinsalu, R. Kitt, and J. Kalda
  Econophysics studies in Estonia
  Journal of Science and Culture (Indian Science News Association) 76(9-10) (2010) 374
  Special issue Sep.-Oct. “Econophysics”
  http://www.scienceandculture-isna.org/sep-oct-2010.htm  
  arXiv:1006.3708

• M. Patriarca, E. Heinsalu, and A. Chakraborti
  Basic kinetic wealth-exchange models: common features and open problems
  Eur. Phys. J. B 73, (2010) 145 
  doi:10.1140/epjb/e2009-00418-6   
  arXiv:physics/06112452

• A. Chakraborti and M. Patriarca
  A variational principle for the Pareto power law
  Phys. Rev. Lett. 103 (2009) 228701  
  doi:10.1103/PhysRevLett.103.228701  
  arXiv:cond-mat/0605325

• A. Chakraborty and M. Patriarca
  Gamma-distribution and wealth inequality
  Pramana J. Phys. 71(2) (2008) 233
  Special Issue: Statistical Physics Approaches to Multidisciplinary Problems
  doi:10.1007/s12043-008-0156-3 
  https://www.ias.ac.in/describe/article/pram/071/02/0233-0243🔓
  arXiv.org:0802.4410

• M. Patriarca, A. Chakraborti, E. Heinsalu, and G. Germano
  Relaxation in Statistical Many-agent Economy Models
  Eur. Phys. J. B 57 (2007) 219  
  doi:10.1140/epjb/e2007-00122-7  
  arXiv:physics/0608174

• M. Patriarca, A. Chakraborti, and G. Germano
  Influence of saving propensity on the power-law tail of wealth distribution
  Physica A 369 (2006) 723  
  doi:10.1016/j.physa.2006.01.091  
  arXiv:physics/0506028

• M. Patriarca, A. Chakraborti, K. Kaski, and G. Germano
  Kinetic theory models for the distribution of wealth: power law from overlap of exponentials
  in: Econophysics of Wealth Distributions, Econophys-Kolkata 1, A. Chatterjee, S.Yarlagadda, B.K. Chakrabarti, Eds., Springer, 2005
  doi:10.1007/88-470-0389-X_10  
  arXiv:physics/0504153

• M. Patriarca, A. Chakraborti, and K. Kaski
  Gibb’s versus non-Gibb’s distributions in money dynamics
  Physica A 340 (2004) 334  
  doi:10.1016/j.physa.2004.04.024  
  arXiv:cond-mat/0312167

• M. Patriarca, A. Chakraborti, and K. Kaski
  A statistical model with a standard Γ-distribution
  Phys. Rev. E 70, (2004) 016104  
  doi:10.1103/PhysRevE.70.016104  
  arXiv:cond-mat/0402200