Experimental realization of an analog of entanglement between two Brownian particles
We experimentally investigate the statistical properties of a classical analog of quantum entanglement considering two Brownian particles connected by an elastic force and maintained at different temperatures through separate heat reservoirs. Uncertainty relations between coordinates and coarse-grained velocity can produce a phenomenon similar to quantum entanglement, where temperature plays the role of Planck's constant. The theoretical analysis matches the experimental results, confirming that the interconnected particles exhibit Brownian quantum-inspired classical correlation entanglement. This effect arises from a coarse-grained description of Brownian motion and vanishes at a finer resolution. The coarsening scales range is measured too.