Dynamic Ramsey Theory of Mechanical Systems Forming a Complete Graph and Vibrations of Cyclic Compounds

Shvalb, Nir; Frenkel, Mark; Shoval, Shraga; Bormashenko, Edward

doi:10.20944/preprints202209.0331.v1

Cited by 3 publications

(3 citation statements)

References 10 publications

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“…And it becomes extremely important for Ramsey-analysis of transitive and non-transitive graphs, representing physical problems; the transitive and nontransitive Ramsey numbers are different [11]. Applications of the Ramsey theory to the analysis physical problems are rare [28,29]; we demonstrate the possibility of these applications in the various sub-fields of fundamental physics.…”

Section: Discussionmentioning

confidence: 87%

Universe as a Graph (Ramsey Approach to Analysis of Physical Systems)

Shvalb¹,

Frenkel²,

Shoval³

et al. 2022

Preprint

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Application of the Ramsey graph theory to the analysis of physical systems is reported. Physical interactions may be very generally classified as attractive and repulsive. This classification creates the premises for the application of the Ramsey theory to the analysis of physical systems built of electrical charges, electric and magnetic dipoles. The notions of mathematical logic, such as transitivity and intransitivity relations, become crucial for understanding of behavior of physical systems. The Ramsey approach may be applied to the analysis of mechanical systems, when actual and virtual paths between the states in configurational space are considered. Irreversible mechanical and thermodynamic processes are seen within the reported approach as directed graphs. Chains of irreversible processes appear as transitive tournaments. These tournaments are acyclic; the transitive tournaments necessarily contain the Hamiltonian path. The set of states in the phase space of the physical system, between which irreversible processes are possible, is considered. Hamiltonian path of the tournament emerging from the graph uniting these states is a relativistic invariant. Applications of the Ramsey theory to the general relativity become possible when the discrete changes in the metric tensor are assumed. Reconsideration of the concept of “simultaneity” within the Ramsey approach is reported.

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Section: Discussionmentioning

confidence: 87%

Universe as a Graph (Ramsey Approach to Analysis of Physical Systems)

Shvalb¹,

Frenkel²,

Shoval³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…16 of 18 physical problems are rare [52,53]; we demonstrate the possibility of these applications in the various sub-fields of fundamental physics.…”

Section: Discussionmentioning

confidence: 88%

Universe as a Graph (Ramsey Approach to Analysis of Physical Systems)

Shvalb¹,

Frenkel²,

Shoval³

et al. 2023

Preprint

View full text Add to dashboard Cite

Application of the Ramsey graph theory to the analysis of physical systems is reported. Physical interactions may be very generally classified as attractive and repulsive. This classification creates the premises for the application of the Ramsey theory to the analysis of physical systems built of electrical charges, electric and magnetic dipoles. The notions of mathematical logic, such as transitivity and intransitivity relations, become crucial for understanding of the behavior of physical systems. The Ramsey theory explains why nature prefers cubic lattices over hexagonal ones for systems built of electric or magnetic dipoles. The Ramsey approach may be applied to the analysis of mechanical systems when actual and virtual paths between the states in the configurational space are considered. Irreversible mechanical and thermodynamic processes are seen within the reported approach as directed graphs. Chains of irreversible processes appear as transitive tournaments. These tournaments are acyclic; the transitive tournaments necessarily contain the Hamiltonian path. The set of states in the phase space of the physical system, between which irreversible processes are possible, is considered. The Hamiltonian path of the tournament emerging from the graph uniting these states is a relativistic invariant. Applications of the Ramsey theory to the general relativity become possible when the discrete changes in the metric tensor are assumed. Reconsideration of the concept of “simultaneity” within the Ramsey approach is reported.

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“…The transitive tournament contains no directed cycles and this is true for any number of vertices/thermodynamic states forming the complete graph [19]. Non-transitive [20,21]. We demonstrate the possibility of such applications in thermodynamics.…”

Section: Theory Of Graphs and Irreversible Thermodynamic Processesmentioning

confidence: 89%

Ramsey Theory and Thermodynamics

Bormashenko¹,

Shvalb²,

Frenkel³

et al. 2022

Preprint

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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.

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Dynamic Ramsey Theory of Mechanical Systems Forming a Complete Graph and Vibrations of Cyclic Compounds

Cited by 3 publications

References 10 publications

Universe as a Graph (Ramsey Approach to Analysis of Physical Systems)

Universe as a Graph (Ramsey Approach to Analysis of Physical Systems)

Universe as a Graph (Ramsey Approach to Analysis of Physical Systems)

Ramsey Theory and Thermodynamics

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