Constantino Tsallis

Theoretical physicist focused on nonextensive statistical mechanics. CBPF researcher and Founder of the National Institute of Science and Technology for Complex Systems of Brazil.
Rio de Janeiro
. Brazil
Contributor Since November 2024

Physicist in the area of statistical mechanics, and former Head of the Department of Theoretical Physics at the Centro Brasileiro de Pesquisas Físicas (CBPF). Founder and former Head of the National Institute of Science and Technology for Complex Systems of Brazil (INCT-Sistemas Complexos) and an external Professor of the Santa Fe Institute, New Mexico and of the Complexity Science Hub Vienna, Austria. Member of the Brazilian, Latin American and European Academies of Sciences. 

Research focused on foundational questions of statistical mechanics through a nonadditive generalization of the Boltzmann-Gibbs entropy (also now frequently referred to as “Tsallis” entropy). This framework has fostered work on a broad range of fascinating theoretical subjects and interdisciplinary collaborations in the areas of critical phenomena, chaos, nonlinear dynamics, population evolution, cognitive psychology, high energy physics, astrophysics and cosmology, immunology and cancer, neuroimaging, economics, amongst others, and resulted in more than 18,000 ISI citations, and more than 1,000 invited lectures around the globe on various research topics.

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October 29, 2025
Editor’s Note: This semi-technical review article is republished with exclusive permission from The Royal Society Press. It was originally published to the peer-reviewed journal Philosophical Transactions of The Royal Society A. This article has a target audience of researchers and experts in diverse disciplines, though to make the content more understandable and engaging for a wider audience, we have broken apart the pdf version of the article into five parts and interspersed audio clips from Constantino Tsallis on relevant topics being discussed in the article. Explore our full InterDialogue with Professor Tsallis to learn more about the development and interdisciplinary applications of his innovative generalized theory of non-additive “Tsallis” entropy and q-statistics. Listen to Tsallis explain about his diverse cultural background and the early development of non-additive entropy. Explore the full InterDialogue with Constantino Tsallis Listen to Tsallis speak about the early presentations, recognitions and interdisciplinary applications of non-additive entropy, the beginning of his collaboration with Murray Gell-Mann, his entrance into the burgeoning field of complex systems and his founding of the National Institute of Science and Technology for Complex Systems (INCT-SC) in Brazil. Explore the full InterDialogue with Constantino Tsallis Listen to Tsallis explain about some of the very broad interdisciplinary applications and collaborations that have been fostered by non-additive entropy and q-statistics, and why he thinks this is possible, from neuroscience and childhood development, to economics to foundational questions of biogenesis and cosmology, all existing “at the edge of chaos.” Explore the full InterDialogue with Constantino Tsallis Listen to Tsallis explain about how non-additive entropy and q-statistics have been observed in medical imaging and the applications for human health, from neuroimaging in children to electrocardiograms in adults. Explore the full InterDialogue with Constantino Tsallis Banner image: Mandelbrot set. The edge of the Mandelbrot set represents the line between...
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Constantino Tsallis
Contributors
September 17, 2026
Over the past two decades, complexity science has matured from its origins as a small, largely esoteric subfield of theoretical statistical physics and mathematics into an expansive area of inquiry that bridges disciplines and addresses some of the world’s most acute interconnected challenges.  Nowhere has this interdisciplinary, applied process become more apparent than with the ongoing convergence of complexity and health.  This convergence is happening at all scales—individual and collective, private and public—across approaches to prevention, treatment, management, and containment in integrative and public health spaces, as well as through applied research and innovation. “Our methodological approach goes on and on down to the level of microbiology and finally finding cures for many diseases,” says Italian American physicist and complex networks scientist Alessandro Vespignani. “All that goes through networks and through a vision that has complex systems at the core. Network science is a way to approach complex systems,” Vespignani explained from within Northeastern University’s Network Science Institute, where he serves as director, leads the Laboratory for the Modeling of Biological and Socio-technical Systems (MOBS) lab, and heads several impactful public health initiatives. “We look at elements and their interactions, and we do not get rid of nonlinear phenomena, feedback loops, et cetera, that exist in real world systems; we need to consider those,” Vespignani continues. “And in that sense, there is even more urgency in the work that we as a community do to respond to those challenges and to be of service to the society.” Explore the full InterDialogue with Alessandro Vespignani. The COVID-19 pandemic served as a critical moment of applied research and broad engagement with public health policy for those, like Vespignani, who work at the interface of complexity and health. But theoretical research and its translation into experiments and action began several years prior and...
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Daniel Henryk Rasolt
January 29, 2026
Is self-organization the answer to the foundational question of why life exhibits such complexity? And can it also serve as a guiding framework for how best to save complex webs of biodiversity amid the onslaughts of the modern world? Self-organization exists throughout nature and socioeconomic structures. It refers to the spontaneous emergence of collective, complex order within a disordered system, due to localized interactions that follow simple rules, and occurring without external controls. While conceptually abstract, given that uncertainty lies at its core, the applications of self-organization are everywhere. Advancing our understanding of the non-linear processes within complex systems that drive self-organization is also becoming increasingly important for developing evidence-based policies in a world defined by interdependence and escalating stressors. Indigenous cultures, such as those that live within complex socio-ecological systems in the Amazon ecoregion, have long embraced these principles of uncertainty, interconnectedness, and non-linear dynamics. How will their wisdom, experience, and models of socio-ecological systems integrate with evidence-based policies for protecting the Amazon ecoregion? Safeguarding the Amazon is one of our world’s most pressing, complex, and vital global challenges. Among the strategies gaining traction, supported by increasing financial investment, is the intriguing proposition to transform a portion of the region’s immense biodiversity into a sustainable “bioeconomy.” However, these proposals, and the policy makers responsible for negotiating their implementation across boundaries and cultures, often lack an understanding of how both economies and ecologies self-organize and scale. Data-driven models of self-organization and critical collective phenomena in the natural world and within traditional Indigenous sociocultural structures, along with adaptive context-based frameworks, can help guide the transboundary development of a decentralized and circular socio-bioeconomy for the Amazon. Self-Organized Criticality and the Edge of Chaos Pioneering research on self-organized criticality (SOC) began in the 1980s and was made accessible to a wider audience by...
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Daniel Henryk Rasolt
November 24, 2025
Investment in science is a pillar for any dynamic, equitable modern society, and promoting scientific literacy across all levels of society can help foster innovation, dialogue, and consensus that crosses disciplinary and cultural boundaries. Science also helps to uncover answers to foundational questions that have captivated, confounded, and divided our species for millennia. But what is “science,” and what kind of “evidence” ensures that an approach is scientific? If we take “science” to broadly mean, in its purest sense, a “dynamic search for the truth,” or more explicitly, “the pursuit and application of knowledge and understanding of the natural and social world following a systematic methodology based on evidence,” as the Science Council aptly defines it, then science extends beyond the established, highly specialized disciplines of reductionist natural sciences (physics, chemistry, biology, geoscience, and space science) that have been so successful in fostering our understanding of our planet and the cosmos. Under this definition, science also includes the rigorous data-driven (qualitative and quantitative) social sciences, the inherently non-reductionist “holistic” sciences such as ecological and Earth system sciences, and the budding interdisciplinary field of complex systems science, as well as robust traditional knowledge systems based on multi-generational experiences, observations, and reasoning. As with science, “evidence” can mean a lot of things as well, including primary research, pre-existing data, past and planned experiments, and the referencing of peer-reviewed publications and primary sources. It can also include local and traditional knowledge, thought experiments, theoretical proofs, contemplation, verifiable personal experience, and empirical observation. Broadening and weaving together these forms of scientific evidence holds the potential to address complex, interconnected global challenges and explain deep mysteries that could help unify our polarized societies around foundational understandings. Foundational Questions Foundational questions can transcend the divides of generations and cultures: Cosmology, physics, and evolutionary biology have shed...
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Daniel Henryk Rasolt

Constantino Tsallis: Non-Additive Entropy, Complexity, Interdisciplinary Collaborations and Beauty

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Constantino Tsallis has joined The Interplex
on November 15, 2024
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