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Explore the physics of Casimir forces through this comprehensive colloquium lecture that examines both equilibrium and non-equilibrium fluctuation-induced interactions. Begin with a historical survey of Casimir physics, tracing its development from the original analysis of zero-point quantum fluctuations in vacuum to its generalization across quantum, thermal, and stochastic contexts. Delve into recent research on equilibrium Casimir forces in Euclidean field theory with higher-order derivative actions, utilizing exact calculations of Feynman path integrals. Examine non-equilibrium steady state Casimir forces in driven electrolyte systems through the lens of Dean-Kawasaki equation-based stochastic dynamic field theory. Gain insights into the mathematical foundations and physical principles underlying these long-range effective interactions, presented by a leading researcher in fluctuation-related physics and mathematics.
