O původu nevratných procesů
Thesis title in Czech:  O původu nevratných procesů 

Thesis title in English:  On the origin of irreversible processes 
Key words:  Nevratnost, entropie, disipace, hamiltonovská evoluce, samoregularizace 
English key words:  Irreversibility, entropy, dissipation, Hamiltonian evolution, selfregularization 
Academic year of topic announcement:  2018/2019 
Type of assignment:  diploma thesis 
Thesis language:  
Department:  Mathematical Institute of Charles University (32MUUK) 
Supervisor:  RNDr. Michal Pavelka, Ph.D. 
Author: 
Guidelines 
1) Formulation of classical mechanics, rigid body motion and reversible fluid mechanics in the Hamiltonian setting (using a Poisson bracket).
2) Selfregularization of classical mechanics using the approach from [1]. Numerical examples. 3) Selfregularization of rigid body motion using the approach from [1]. Numerical examples. 4) Selfregularization of fluid mechanics using the approach from [1]. Numerical examples. 5) Discussion of Landau damping [1]. 6) Discussion of the origin of the second law of thermodynamics comparing [1] and [2]. 
References 
[1] Michal Pavelka, Václav Klika and Miroslav Grmela, Statistical mechanics of Landau damping, Submitted to Entropy (2018)

Preliminary scope of work in English 
Hamilton canonical equations, which describe evolution within classical mechanics, are completely reversible. Assuming that macroscopic systems around us can be approximated as systems of classical particles, evolution of the systems can be also described by reversible classical mechanics.
On the other hand, processes that the macroscopic systems undergo are typically irreversible (friction, diffusion, temperature equilibration, etc.). The question is from where this irreversibility comes from. Why does entropy of an isolated system grow in time? What is the reason behind the second law of thermodynamics? 