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.
- Mark Peletier Eindhoven University of Technology, The Netherlands
- Grigorius A. Pavliotis Imperial College London, United Kingdom
- Hans Christian Öttinger ETH Zurich, Switzerland
- Mark Peletier Eindhoven University of Technology, The Netherlands
