Topic 5. Fundamental underpinnings and rigorous mathematical results

Nonequilibrium thermodynamics may be regarded as a framework for constructing, identifying, and understanding healthy time-evolution equations for coarse-grained systems. This requires a deep understanding, both formal and rigorous, of the relationship between microscopic models and their coarse-grained relatives. The Hamiltonian structure of reversible dynamics is well-understood. Our focus hence is on understanding the mathematical structure(s) associated with irreversible dynamics as well as the combination of reversible and irreversible dynamics.

For this topic we envision contributions dealing with:

• Formulation of mathematical structure(s) for time-evolution equations.
• Results for the mathematical structure(s) emerging from many-to-one transformations (coarse graining, emergence of irreversibility, large deviations).
• Alternatives to the projection-operator formalism for separating time scales.
• Rigorous results for nonequilibrium entropy and related functionals.
• Proofs for the existence and uniqueness of solutions of time-evolution equations based on thermodynamic ingredients.
• Development of numerical integration methods respecting thermodynamic structure.
• Proper mathematical description of fluctuations.
• Generalizations to dissipative quantum systems.

Teachers (Summer school)

• Mark Peletier   Eindhoven University of Technology, The Netherlands
• Grigorius A. Pavliotis   Imperial College London, United Kingdom

Topic organizers

• Hans Christian Öttinger   ETH Zurich, Switzerland
• Mark Peletier   Eindhoven University of Technology, The Netherlands

2025