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thermodynamics equilibrium state vs. steady state???

I am not clear about two concepts: thermodynamics equilibrium state and steady state. It's easy to conceive of the following different two osmosis processes regarding thermodynamics equilibrium state and steady state, respecitvely.

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Does there exist a negative dimensionless quantity?

att.

 I am just wondering if there exists a negative dimensionless quantity? It seems that all dimensionless numbers I encount in my field (fluid dynamics) are positive. what if it is negative? and if negative, what does that mean? I sense that:

the imposed negative sign for a dimensionless number is just an alternative expression for a special external boundary condition, rather than no longer a characteristics over an essential in a physical law that required for being independent of external boundary conditions.

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Is it possible to define a dimensionless number being capable of characterizing the two effects with totally opposite direction?

1. assuming to exist a PDE describing an equilibrium along one direction (e.g., postive direction along X coordinate), A+B=0;

2. after normalization process to the above PDE, we got, A*+(C)B*=0;

3. (C)=B/A, is the dimensionless number, and obviously, (C) implicits that both two effects arising from A and B are the same in the direction, i.e., along the X positive coordanate;

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