NOBEL SYMPOSIUM 215 — Beyond Boltzmann: Complexity, Memory, and Non-Additive Entropies

24 May 2027, 15:30 → 28 May 2027, 17:35 Europe/Stockholm

Conference room (Bäckaskog slott)

Roman Pasechnik (Lunds universitet)

Hosted by the Department of Physics, Lund University · Division symposium page

How do memory, strong correlations and global constraints shape the statistical laws of complex systems?

Researchers across statistical physics, particle physics, quantum information and data-rich sciences will examine the foundations, mechanisms and evidence for generalized entropies. The aim is to connect ideas across disciplines, assess their physical scope and identify decisive tests.

Scientific programmeFull timetableInvited speakersPublic lecture

The Nobel Symposia tradition

Established in 1965, NOBEL SYMPOSIA bring leading Swedish and international researchers together for scientific exchange at a high level. These compact, invitation-only meetings examine advances in rapidly developing fields, clarify open questions and identify future research priorities, with an emphasis on in-depth discussion and clear scientific outcomes.

A shared foundation for complex systems

Boltzmann–Gibbs statistical mechanics provides a powerful reference for understanding collective behaviour. Systems with persistent memory, slow mixing, long-range interactions or restricted access to microscopic states raise further questions: which entropy is appropriate, how does it arise from the dynamics, and what can observations establish?

Six plenary sessions, 29 planned talks and six hours reserved for scientific discussion create a common programme. Each session includes two dedicated 30-minute discussions; rapporteurs bring the main conclusions and open questions to Friday’s synthesis.

S1 · Foundations

Admissible generalized entropies and thermodynamic consistency.

S2 · Dynamics

Weak chaos, memory and anomalous transport.

S3 · Physical tests

Many-body systems, turbulence and granular matter.

S4 · Particle physics

Nonextensivity, self-similarity and high-energy collisions.

S5 · Quantum theory & gravity

Quantum information, black holes and cosmology.

S6 · Data-rich systems

AI and complex systems beyond traditional physics.

The week at a glance

Preliminary programme · all times local to Sweden

Day	Programme	Location
Monday 24 May	Arrival, opening reception, coach transfer and welcome dinner	Lund → Bäckaskog
Tuesday 25 May	Scientific opening; S1 Foundations; S2 Dynamics	Bäckaskog
Wednesday 26 May	S3 Physical tests; S4 Particle physics; early-career forum	Bäckaskog
Thursday 27 May	S5 Quantum theory and gravity; S6 Data-rich systems; banquet	Bäckaskog
Friday 28 May	Rapporteur summaries, Round Table and Symposium Statement; return to Lund; public lecture	Bäckaskog → Lund

Taking part

Participation in the scientific symposium, including early-career participation, is by invitation. The week brings researchers together from the opening reception in Lund on Monday 24 May to the scientific closing at Bäckaskog at noon on Friday 28 May. A dedicated early-career forum provides time for short presentations and scientific exchange.

Registration details will be sent directly to invited participants. The private Indico form will collect attendance, accommodation and transport requests for coordination with Reachem, the symposium’s conference agency. See Venue and travel for practical arrangements.

The Friday public lecture, What is Entropy? by Constantino Tsallis, is a separate event for a wider audience.

Scientific contact: Roman Pasechnik · Constantino Tsallis.

Nobel Symposium 215

Host: Department of Physics

Nobel Symposium 215: Beyond Boltzmann: Complexity, Memory, and Non-Additive Entropies was funded by the Royal Swedish Academy of Sciences and organised by the Department of Physics, Lund University.

The NOBEL SYMPOSIA mark is owned by the Nobel Foundation.

Monday 24 May

15:30 → 16:00 Registration and arrival

Registration before the opening reception in Lund.

16:00 → 17:00 Opening reception and Lund University welcome

Opening reception, hosted by Roman Pasechnik and Constantino Tsallis. Welcome address by Vice-Chancellor Erik Renström at approximately 16:15.

Speaker: Erik Renström (Lund University, Vice-Chancellor)

17:15 → 18:45 Coach transfer: Lund → Bäckaskog slott

Organised coach transfer following the opening reception. The coach is provisionally booked for 50 participants; capacity will be adjusted once attendance is confirmed.

19:30 → 21:00 Welcome dinner — end time indicative

Welcome dinner begins at 19:30 at Bäckaskog slott. The 21:00 end time is indicative.

Tuesday 25 May

08:45 → 09:15 Welcome and scientific opening

Introduction to the scientific aims, programme and discussion format.

09:15 → 13:30 S1 · Foundations and admissible generalized entropies: Chair to be confirmed · Rapporteur: Tamás S. Biró

Definitions, admissibility, composability and thermodynamic consistency establish the common language of the symposium. Topics include generalized entropy classes, accessible-state scaling, group entropies, superstatistics and the foundations of nonextensive statistical mechanics.

Discussion focus: Which generalized entropies are physically meaningful, under what conditions do they apply, and which observations distinguish among them?

09:15 From Boltzmann–Gibbs to nonadditive entropies: foundations, scope and decisive tests

Preliminary talk title. Abstract and key references to follow.

Opening keynote: 40 minutes followed by 5 minutes for clarification.

Speaker: Constantino Tsallis (CBPF)

10:00 Superstatistics and the dynamical emergence of q-statistics

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Christian Beck (Queen Mary University of London)

10:30 Universality classes and generalized entropies for complex, nonergodic systems

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Stefan Thurner (Medical University of Vienna / CSH)

11:00 S1 discussion 1

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Celia Anteneodo. Rapporteur: Tamás S. Biró.

11:30 Coffee break (S1)

12:00 Group entropies and the classification of admissible entropic functionals

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Piergiulio Tempesta (Universidad Complutense de Madrid / ICMAT)

12:30 Nonequilibrium statistical mechanics foundations of nonextensive statistical mechanics

Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Evaldo M. F. Curado (CBPF)

13:00 S1 discussion 2

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Celia Anteneodo. Rapporteur: Tamás S. Biró.

13:30 → 14:30 Lunch

14:30 → 18:30 S2 · Weak chaos, memory and anomalous transport: Chair: Andrea Rapisarda · Rapporteur: Henrik Johannesson

Dynamical routes to q-statistics through edge-of-chaos scaling, slow mixing, memory and nonlinear diffusion. Low-dimensional maps, Hamiltonian lattices and nonlinear Fokker–Planck descriptions connect microscopic dynamics to statistical limit laws and anomalous transport.

Discussion focus: How do these mechanisms generate non-Boltzmann statistics, and how can finite-time effects, finite-size effects and competing explanations be tested?

14:30 The edge of chaos: renormalization-group dynamics and q-statistics

Speaker confirmation pending. Preliminary topic; abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

15:00 The Importance of Tsallis Thermostatistics in the Study of 1-dimensional Hamiltonian Lattices

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Anastasios Bountis (University of Patras)

15:30 Universality and q-statistical limit laws in low-dimensional maps

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Uğur Tirnakli (İzmir University of Economics)

16:00 S2 discussion 1

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Andrea Rapisarda. Rapporteur: Henrik Johannesson.

16:30 Coffee break (S2)

17:00 Anomalous Diffusion Beyond Boltzmann–Gibbs

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Celia Anteneodo (PUC-Rio)

17:30 Nonlinear Fokker–Planck equations and anomalous nonextensive dynamics

Speaker confirmation pending. Preliminary topic; abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

18:00 S2 discussion 2

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Andrea Rapisarda. Rapporteur: Henrik Johannesson.

19:30 → 21:00 Dinner — end time indicative

Dinner begins at 19:30. The 21:00 end time is indicative and will be updated when arrangements are confirmed.

Wednesday 26 May

09:00 → 13:00 S3 · Many-body systems, turbulence and granular matter: Chair: Anastasios Bountis · Rapporteur: Alessandro Pluchino

Correlated many-body systems provide physical tests of generalized statistical descriptions. Topics span turbulence, q-Gaussian spectral crossovers in glasses and correlated random matrices, controlled granular experiments, long-range Hamiltonian quasi-stationary states and turbulent plasma kinetics.

Discussion focus: Connecting mechanisms to experiments, simulations and observations, and establishing decisive benchmarks across these systems.

09:00 Superstatistics, intermittency and circulation fluctuations in turbulence

Speaker confirmation pending. Preliminary topic; abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

09:30 q-Gaussian spectral crossovers in correlated systems: glasses and random matrices

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Abbas Ali Saberi (Constructor University)

10:00 S3 discussion 1

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Anastasios Bountis. Rapporteur: Alessandro Pluchino.

10:30 Coffee break (S3)

11:00 Experimental nonextensive scaling in confined granular matter

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Gaël Combe (Université Grenoble Alpes)

11:30 Long-range Hamiltonian systems: quasi-stationary states and anomalous dynamics

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Andrea Rapisarda (University of Catania)

12:00 First-principles q-statistics in turbulent plasmas: from kinetic theory to spacecraft verification

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Peter H. Yoon (University of Maryland)

12:30 S3 discussion 2

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Anastasios Bountis. Rapporteur: Alessandro Pluchino.

13:00 → 14:00 Lunch

14:00 → 17:30 S4 · Nonextensivity in particle physics: Chair: Roman Pasechnik · Rapporteur: Bo-Sture Skagerstam

Non-exponential laws in particle and heavy-ion collisions connect statistical descriptions with strongly interacting matter. Topics include q-exponential spectra, thermofractality and QCD self-similarity, femtoscopy, finite or fluctuating reservoirs, composition laws and transport in hot and magnetized QCD matter.

Discussion focus: Which microscopic mechanisms account for observed statistical laws, and which collision observables discriminate among their interpretations?

14:00 Thermofractals, QCD self-similarity and nonextensive hadron thermodynamics

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Airton Deppman (University of São Paulo)

14:30 Heavy tails and Tsallis phenomenology in high-energy collisions and femtoscopy

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Tamás Csörgő (HUN-REN Wigner RCP / MATE)

15:00 S4 discussion 1

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Roman Pasechnik. Rapporteur: Bo-Sture Skagerstam.

15:30 Coffee break (S4)

16:00 From nonextensive ideal gases to group entropy: finite phase space and the formal logarithm

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Tamás S. Biró (HUN-REN Wigner RCP)

16:30 Nonextensive transport in hot and magnetized QCD matter

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Sadhana Dash (IIT Bombay)

17:00 S4 discussion 2

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Roman Pasechnik. Rapporteur: Bo-Sture Skagerstam.

17:45 → 18:50 Early-career researcher forum

Three-minute presentations by early-career observers, followed by questions and feedback from senior participants. Coordinator: Alessandro Pluchino.

19:30 → 21:00 Dinner — end time indicative

Dinner begins at 19:30. The 21:00 end time is indicative and will be updated when arrangements are confirmed.

Thursday 27 May

09:00 → 13:00 S5 · Quantum information, black holes and cosmology: Chair: Bo-Sture Skagerstam · Rapporteur: Ángel Luis Plastino

Quantum theory and gravity bring distinct questions about entropy into view. Topics include generalized information measures, Tsallis and Rényi entropies, group entropies, horizon thermodynamics, holography and cosmological tests. Routes to extensivity through generalized variables, formal logarithms or additional work terms will be compared.

Discussion focus: Distinguishing thermodynamic consistency from quantum-information questions, and identifying theoretical or observational tests of alternative descriptions.

09:00 Generalized entropy, gravity and cosmology: consistency and observational tests

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Petr Jizba (Czech Technical University in Prague)

09:30 Universality classes and thermodynamics of group entropies: extensivity, composability and black holes

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Henrik J. Jensen (Imperial College London)

10:00 Quantum Tsallis and Rényi entropies: continuity, coherence and information constraints

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Anna Vershynina (University of Houston)

10:30 S5 discussion 1

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Bo-Sture Skagerstam. Rapporteur: Ángel Luis Plastino.

11:00 Coffee break (S5)

11:30 Nonadditive holographic dark energy and current cosmological constraints

Speaker confirmation pending. Preliminary topic; abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

12:00 Holographic Rényi entropies: generalized information measures from black-hole thermodynamics

Speaker confirmation pending. Preliminary topic; abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

12:30 S5 discussion 2

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Bo-Sture Skagerstam. Rapporteur: Ángel Luis Plastino.

13:00 → 14:00 Lunch

14:00 → 18:00 S6 · AI and data-rich complex systems beyond traditional physics: Chair: Tiziana Di Matteo · Rapporteur: Henrik J. Jensen

The final thematic session tests generalized statistical ideas beyond traditional physics. Topics include sparse machine learning, nonlinear prediction, complex networks, data-rich ecosystems and statistical seismology, under the same standards of mechanism and evidence used throughout the symposium.

Discussion focus: How are entropy and composability structures realized in networked and data-rich systems, and when do they improve understanding or prediction relative to alternative models?

14:00 Tsallis α-entropies in machine learning: entmax, sparse attention and Fenchel–Young losses

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: André F. T. Martins (Instituto Superior Técnico / IT)

14:30 Nonlinear dynamics and machine learning for prediction in complex systems

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Ying-Cheng Lai (Arizona State University)

15:00 S6 discussion 1

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Tiziana Di Matteo. Rapporteur: Henrik J. Jensen.

15:30 Coffee break (S6)

16:00 Invited contribution — title and speaker to be confirmed

Speaker confirmation pending. Preliminary topic; abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

16:30 Heavy tails and scaling in data-rich ecosystems: financial markets, company transaction networks and gut microbiome

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Misako Takayasu (Institute of Science Tokyo)

17:00 Nonextensive statistical seismology: criticality, hazards and decisive observables

Preliminary talk title. Abstract and key references to follow.

Presentation: 25 minutes followed by 5 minutes for questions.

Speaker: Filippos Vallianatos (National and Kapodistrian University of Athens)

17:30 S6 discussion 2

Dedicated discussion of the preceding talks: mechanisms, evidence, unresolved questions and decisive tests.

Chair: Tiziana Di Matteo. Rapporteur: Henrik J. Jensen.

18:00 → 18:45 Group photo and optional guided walk

Group photo followed by an optional guided walk at Bäckaskog slott.

19:30 → 21:00 Symposium banquet — end time indicative

The banquet begins at 19:30. The 21:00 end time is indicative. The banquet venue will be confirmed.

Friday 28 May

09:00 → 09:50 Six rapporteur summaries

About eight minutes per session: points of agreement, unresolved alternatives, proposed tests and priorities.

Rapporteurs: Tamás S. Biró (S1), Henrik Johannesson (S2), Alessandro Pluchino (S3), Bo-Sture Skagerstam (S4), Ángel Luis Plastino (S5) and Henrik J. Jensen (S6).

09:50 → 10:20 Coffee break

10:20 → 11:35 Scientific Synthesis Round Table

Common language, decisive tests and priorities for the years ahead, including whether “non-extensivity” remains the appropriate shared term when extensivity is restored in generalized variables.

The Scientific Synthesis Panel integrates the six rapporteur syntheses. Moderator: Roman Pasechnik. Scientific Secretary: Tiziana Di Matteo, recording agreements, unresolved alternatives, tests and actions.

11:35 → 11:50 Symposium Statement: plenary consideration and adoption

Plenary consideration and adoption of a short closing text prepared by the Scientific Synthesis Panel from the six rapporteur syntheses and the Round Table. The Statement will inform the planned open-access Symposium Report.

11:50 → 12:00 Closing remarks

The closed scientific programme ends at noon.

12:00 → 12:40 Early lunch

12:45 → 14:15 Coach transfer: Bäckaskog → Science Village / Lund

Organised coach transfer to the Lund programme. The final route and drop-off arrangements will be confirmed.

14:15 → 15:15 Optional ESS / MAX IV visit — facility to be confirmed

Optional visit associated with ESS / MAX IV at Science Village. Facility, access requirements and final arrangements will be confirmed.

15:45 → 16:15 Public lecture: doors open and Swedish fika

Doors open at 15:45, with Swedish fika before the public lecture at 16:15. The lecture venue and admission arrangements will be announced.

16:15 → 17:15 What is Entropy?

Public lecture by Constantino Tsallis, separate from the closed scientific symposium. Venue, admission arrangements and the Lund University introduction will be announced when confirmed.

Speaker: Constantino Tsallis (CBPF)

17:15 → 17:35 Public questions and farewell

Questions following the public lecture and farewell.

Speaker: Constantino Tsallis (CBPF)