| Abstract: |
| We reconsider the problem of coarse-graining a microscopic Hamiltonian dynamics which describes the motion of molecules to obtain a macroscopic system which includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning Hamiltonians, energy, and entropy and the induced geometric structures. Randomness enters through the initial data of a heat bath component of the original Hamiltonian system.
The analysis uses some mathematical tools from the theory of dilations, which will be described at the hand of an example.
The main interest is, however, to analyse the resulting system in the formulation of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling). We will show that
the coarse-grained version has this structure, with conserved energy, nondecreasing entropy and an Onsager operator describing the dissipation. A particular interest will be to understand how the building blocks of GENERIC arise from the microscopic Hamiltonian system. |
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