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Ramsey theory and thermodynamics.

Nir Shvalb1, Mark Frenkel2, Shraga Shoval3

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Area of Science:

  • Thermodynamics
  • Graph Theory
  • Ramsey Theory

Background:

  • Thermodynamic states can be attainable or non-attainable.
  • Understanding cycles in thermodynamic processes is crucial.
  • Existing models may not fully capture complex state transitions.

Purpose of the Study:

  • To reshape thermodynamics using graph theory and Ramsey theory.
  • To determine the conditions for thermodynamic cycles in discrete states.
  • To analyze directed graphs of irreversible thermodynamic processes.

Main Methods:

  • Utilizing graph theory to map thermodynamic states.
  • Applying Ramsey theory to find the conditions for cycles.
  • Analyzing complete directed graphs and transitive tournaments.

Main Results:

  • Ramsey theory provides the answer to graph size for guaranteed cycles.
  • Hamiltonian paths are found in complete directed graphs of thermodynamic states.
  • Transitive thermodynamic tournaments are acyclic, containing no directed cycles.

Conclusions:

  • Graph and Ramsey theories offer a new framework for thermodynamics.
  • The structure of thermodynamic processes can be rigorously analyzed using graph properties.
  • Irreversible processes within transitive tournaments do not form cycles.