Abstract
Bistability is often encountered in association with dissipative systems far from equilibrium, such as biological, physical, and chemical phenomena. There have been various attempts to theoretically analyze the bistabilities of dissipative systems. However, there is no universal theoretical approach to determine the development of a bistable system far from equilibrium. This study shows that thermodynamic analysis based on entropy production can be used to predict the transition point in the bistable region during Rayleigh–Bénard convection using the experimental relationship between the thermodynamic flux and driving force. The bistable region is characterized by two distinct features: the flux of the second state is higher than that of the first state, and the entropy production of the second state is lower than that of the first state. This thermodynamic interpretation provides new insights that can be used to predict bistable behaviors in various dissipative systems.
Highlights
Many attempts have been made to identify a universal function whose extremum determines the development of a system far from equilibrium
Analysis based on MEPP can be used to predict the transition point between two nonequilibrium states, such as those observed in the morphological changes of crystal growth, mode changes in droplet oscillation, and pattern changes in thermal convection [12,17,18,19]
In the case of friction phenomena in the flow field, fluid velocity is treated as thermodynamic flux, and the transition point is predicted
Summary
Many attempts have been made to identify a universal function whose extremum determines the development of a system far from equilibrium. For a pendant droplet that changes in the oscillation mode induced by the solutal Marangoni effect with viscous dissipation, the transition point of the oscillation mode is predicted from the intersection of the entropy-production curves determined from the velocity of the oscillating droplet, which is considered as thermodynamic flux [18]. It should be noted that when entropy production is expressed as a function of X, σ(X) cannot distinguish between the nonequilibrium states because all σ(X) are present on a single quadratic curve σ(X) = LX2 [19], where L is the phenological coefficient [1]. We cannot predict the transition point nor even understand whether another kind of nonequilibrium state exists in the system when the thermodynamic flux expressed as a function of the driving force can be described only on a single line. (a) Relationship between convective heat flux averaged over2.one cycle Jconv and ε0 , as presented in [20]
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