Entropic forces mediated by quantum gases 

When particles are coupled to a many-body system, effective forces can emerge between them due to the collective response of the many-body mediator as it tends to maximize its entropy. This is in contrast to fundamental forces that are mediated by the exchange of virtual field quanta. Motivated by our initial work on quasistatic entropic forces [1], we explore the nature of entropic forces in local equilibrium systems such as gases. We study the interplay of entropic forces between masses coupled to a Bose Einstein condensate (BEC) and the propagation of coherent wave-like disturbances in the BEC which lead to dynamic forces between the massive particles. We analyze the effects of the thermal fluctuations of the many-body mediator on the static and dynamic forces between the particles in the thermodynamic limit. Finally, we provide detailed calculations for experimentally observable quantities such as the stochastic noise associated with these emergent forces and waves, thereby extending previous work on entropic forces and waves in fully quantum mechanical systems.

[1] Carney, D., Karydas, M., Scharnhorst, T., Singh, R., & Taylor, J. M. (2025). On the quantum mechanics of entropic forces. Physical Review X, 15(3), 031038.