MP, *Cycle/cocycle oblique projections on oriented graphs*,

Lett. Math. Phys. **105 **, 89-107 (2015). arXiv:1405.0899

Stationary thermodynamic machines proceed in cycles: e.g. the Diesel cycle is completed thousands times per second in each piston of the engine of cars running at a steady speed. However, when processes are not stationary, or when there are external inputs of resources (fuel), cycles do not properly describe the physics of the system, and the onset of transient and time-dependent behavior calls for a refined description. In this paper I investigate the mathematical structure of cycles (characterizing stationary behavior) and of a complementary structure called cocycles, in the special case where thermodynamic processes can be represented as diffusions on graphs. A rich mathematical structure ensues based on the algebraic structure of oblique projections on oriented graphs, which provides a novel contribution to the field of algebraic graph theory.

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