Entropy increase in dissipative systems

[Bob S]

Consider the following steady-state dissipative system. A mountain stream flowing 1 liter per second drops 100 meters over rocks and boulders, and at the bottom has both a temperature increase and a residual kinetic energy (velocity). The sum of the temperature rise and the kinetic energy is 980 watts. Maximum entropy increase would maximize the temperature rise, but because the stream has kinetic energy at the bottom, the temperature rise is not maximum. If I added rocks to the flow, the system constraints and the temperature rise would be higher. What is the over-riding principle that minimizes the entropy increase (maximizes the kinetic energy), based on the constraints of the system?

 

[Bob S]

In this steady state dissipative system, the additional constraint causes a larger heat dissipation and lower final state kinetic energy. The entropy increase is a minimum, subject to the constraints. I always thought that the entropy increase should be maximal, subject to the constraints. Which is correct?
Bob S

 

[astrokreng]

The over-riding principle that minimizes the entropy increase in this system is the principle of energy conservation. This principle states that in a closed system, energy cannot be created or destroyed, but can only be transformed from one form to another. In the case of the mountain stream, the initial potential energy of the water at the top of the mountain is converted into kinetic energy as it flows down the rocks and boulders, and this kinetic energy is then partially converted into thermal energy at the bottom. However, the total amount of energy (980 watts) remains constant.

Therefore, in order to minimize the entropy increase, the system must maximize the conversion of potential energy into kinetic energy. This is because kinetic energy is a more ordered form of energy than thermal energy, and therefore has a lower entropy. By adding rocks to the flow, the system constraints are changed, allowing for a more efficient conversion of potential energy into kinetic energy, resulting in a lower overall entropy increase.

In summary, the principle of energy conservation is the driving force behind the minimization of entropy increase in dissipative systems. By maximizing the conversion of potential energy into kinetic energy, the system is able to maintain a higher level of order and decrease the overall entropy increase.