Abstract
We discovered an out-of-equilibrium transition in the ideal gas between two walls, divided by an inner, adiabatic, movable wall. The system is driven out-of-equilibrium by supplying energy directly into the volume of the gas. At critical heat flux we have found a continuous transition to the state with a low-density, hot gas on one side of the movable wall and a dense, cold gas on the other side. Molecular dynamic simulations of the soft-sphere fluid confirm the existence of the transition in the interacting system. We introduce a stationary state Helmholtz-like function whose minimum determines the stable positions of the internal wall. This transition can be used as a paradigm of transitions in stationary states and the Helmholtz-like function as a paradigm of the thermodynamic description of these states.
Highlights
We discovered an out-of-equilibrium transition in the ideal gas between two walls, divided by an inner, adiabatic, movable wall
We have found a continuous transition to the state with a low-density, hot gas on one side of the movable wall and a dense, cold gas on the other side
Equilibrium thermodynamics provides a clear definition of a few macroscopic variables defining the equilibrium state and function, which has a minimum at this state
Summary
We provide a derivation of the energy of the system Eq (1) and of subsystems Eq (5). Since the movable wall model is assumed to be infinite in y and z directions, it is sufficient to consider the dependence in x direction, so one has. We provide a derivation of the transition point λcL2/kT of the movable wall model with N1 = N2 = N/2, where it is stated that λcL2/kT ≈ 4.55344. For this movable wall model with equal subsystem particles, the phase transition occurs when the number of solutions transit from 1 to 2. This means that the number of times 1(xw) crosses with 2(xw) in xw ≥ 0 transit from 1 to 2, which is equivalently the crossings of G(x) with the x-axis.
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