Ramsey theory and thermodynamics

Nir Shvalb; Mark Frenkel; Shraga Shoval; Edward Bormashenko

doi:10.1016/j.heliyon.2023.e13561

Ramsey theory and thermodynamics

Heliyon. 2023 Feb 10;9(2):e13561. doi: 10.1016/j.heliyon.2023.e13561. eCollection 2023 Feb.

Authors

Nir Shvalb¹, Mark Frenkel², Shraga Shoval³, Edward Bormashenko²

Affiliations

¹ Department of Mechanical Engineering & Mechatronics, Faculty of Engineering, Ariel University, P.O.B.3, Ariel, 407000, Israel.
² Chemical Engineering Department, Engineering Faculty, Ariel University, P.O.B. 3, 407000 Ariel, Israel.
³ Department of Industrial Engineering and Management, Faculty of Engineering, Ariel University, P.O.B. 3, Ariel 407000, Israel.

Abstract

Re-shaping of thermodynamics with the graph theory and Ramsey theory is suggested. Maps built of thermodynamic states are addressed. Thermodynamic states may be attainable and non-attainable by the thermodynamic process in the system of constant mass. We address the following question how large should be a graph describing connections between discrete thermodynamic states to guarantee the appearance of thermodynamic cycles? The Ramsey theory supplies the answer to this question. Direct graphs emerging from the chains of irreversible thermodynamic processes are considered. In any complete directed graph, representing the thermodynamic states of the system the Hamiltonian path is found. Transitive thermodynamic tournaments are addressed. The entire transitive thermodynamic tournament built of irreversible processes does not contain a cycle of length 3, or in other words, the transitive thermodynamic tournament is acyclic and contains no directed thermodynamic cycles.

Keywords: Directed graph; Graph theory; Irreversible process; Ramsey theory; Thermodynamics.