The quasi-equilibrium state: A tale of certain soundless systems

We consider a 1D system with purely non-linear interactions such that no acoustic propagation is possible, We show that our system can attain an equilibrium-like state, which we call the "quasi-equilibrium" state. The quasi-equilibrium state is found to be independent of the initial conditions with the particle velocities satisfying a Gaussian velocity distribution, However, in the absence of sound propagation in the system, no energy equi-partitioning is achieved, Our system shows huge temperature fluctuations, Linear response theory seems inapplicable in describing the propagation of a perturbation in the quasi-equilibrium state.