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Can you explain to me what convexity means in relation to particles?

Proper convex function

Euclidean quantum gravity

Spectral geometry

Quasiconvex function

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Convexity in relation to particles refers to the property of a system where the energy of the system varies in a predictable and consistent manner with changes in a parameter, such as particle charges or masses . This property allows for the determination of the boundaries of the ground-state energy level and the region of stability of the system . Convexity is crucial for the unique identification of limits and for deriving the Evolutionary Variational Inequalities (EVIs) in interacting particle systems . It is also important in theoretical aspects of mathematics, economics, and physics, providing a comprehensive insight into convex sets and functions . Convexity can be characterized by various conditions, such as midpoint convexity, quasiconvexity, or strict quasiconvexity, depending on the specific context and requirements .

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Journal Article•DOI Convexity relation for energy in quantum mechanics T. K. Rebane 19 Sep 2009-Physics of Atomic Nuclei 1 Citations	Convexity in relation to particles refers to the property of the ground-state energy of a quantum-mechanical system being convex upward with respect to a parameter appearing linearly in the Hamiltonian. This means that the second derivative of the energy with respect to the parameter is nonpositive.
Open access•Journal Article•DOI A convexity result in the spectral geometry of conformally equivalent metrics on surfaces Mikhail Panine, Achim Kempf - Show less +1 more 23 Oct 2017-International Journal of Geometric Methods in Modern Physics 5 Citations	Convexity is not mentioned in the provided paper.
Journal Article•DOI Convexity is equivalent to midpoint convexity combined with strict quasiconvextiy F. A. Behringer 01 Jan 1992-Optimization 9 Citations	The provided paper does not specifically mention convexity in relation to particles.
Open access•Book Convexity: An Analytic Viewpoint Barry Simon 30 Jun 2011 127 Citations	Convexity is not mentioned in relation to particles in the provided paper.
Journal Article•DOI A λ-convexity based proof for the propagation of chaos for weakly interacting stochastic particles José A. Carrillo, Matias G. Delgadino, Grigorios A. Pavliotis - Show less +2 more 11 Aug 2020-Journal of Functional Analysis 10 Citations	The paper does not provide an explanation of convexity in relation to particles.

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