Nobel Symposium NS215 — Beyond Boltzmann: Complexity, Memory, and Non-Additive Entropies

Beyond Boltzmann: 
Complexity, Memory, and Non-Additive Entropies

For one and a half centuries, the additive Boltzmann-Gibbs-von Neumann-Shannon (BG) entropy has anchored statistical mechanics and explained an enormous range of phenomena in systems that forget their past quickly and whose accessible microstates grow essentially exponentially with system size. Across today’s data-rich sciences, however, we increasingly meet regimes where space-time correlations decay slowly, memory persists, constraints and long-range couplings crucially matter, and additivity no longer captures the regularities seen in experiments and simulations. Over the last four decades a generalised theory grounded on nonadditive entropies has matured that links weak chaos and criticality to thermodynamics, derives non-exponential laws with uncertainty control, and offers concrete mechanisms for power-law behaviour.

Why now? Three advances align. First, high-quality datasets document robust departures from exponential baselines in laboratory, natural, and engineered systems. Second, theory has clarified thermodynamic consistency, limit theorems, and the role of memory, non-local constraints, and boundary conditions in selecting the appropriate entropic functional. Third, modern inference and machine learning (including Artificial Intelligence) allow head-to-head comparison of exponential and power-law models.

Key questions drive current research. Under what circumstances do boundary conditions and global constraints change the effective entropic functional? How is the zeroth law extended beyond overdamped many-body dynamics to conservative Hamiltonian in classical and quantum systems? When and how do weak chaos (e.g., at the edge of chaos) and long memory reshape equilibration, fluctuation relations, and transport laws?

These developments span condensed- and soft-matter physics, astrophysical and cosmological plasmas, high-energy collisions, neuroscience, earth systems, and complex networks. The field is converging on shared concepts and standards and is ready for consolidation through common benchmarks, reference datasets, and a clear roadmap for the decade ahead.

Participation is by invitation. A limited number of early-career observers will be included through a structured flash session and mentoring round-table.

Preliminary programme

Over four days, with about 50 active participants, the Symposium builds a shared foundation and consolidates recent advances.

Day 1 defines the language of complexity and non-extensive statistical mechanics, clarifying where Boltzmann–Gibbs theory applies and where slow relaxation, long-range couplings, boundary constraints, and initial conditions motivate generalised entropic functionals.

Day 2 presents leading results from arenas where these ideas are explanatory: long-range and overdamped many-body systems; soft and granular matter; quantum-tunneling chemical reactions; space and laboratory plasmas; high-energy collisions; cosmological and astrophysical datasets; complex networks; data-rich urban and biological systems, including medical applications.

Day 3 examines mechanisms — memory, weak chaos and criticality — and implications for equilibration, transport and fluctuation relations, including the status of the zeroth law in Hamiltonian and quantum settings.

Day 4 is for synthesis and consolidation: brief rapporteur summaries; an editorial round-table focusing on terminology, universal characteristics and paradigmatic systems; a chaired drafting session appointing an editor-in-chief, co-editors and section leads; and a closing plenary endorsing a short Symposium Statement and a practicable medium-term outlook focusing on priorities and cross-disciplinary impact. 

Besides, a public lecture "What is Entropy?" by Prof. Tsallis engages the wider community, while a short early-career session fosters structured interaction between young researchers and senior experts.