# Prigogine's theorem of minimum entropy production (Pentcho Valev)

Thu Nov 6 04:00:29 EST 1997

```Bryant Fujimoto wrote:
The problem is that the flux (or flow) is defined to be the             <
rate of change of a thermodynamic variable, in this case the            <
concentration.  Therefore dC(S2)/dt is the definition of J and /4/      <
is correct for steady state.  Somebody decided that a good name for     <
expressions like dC(S2)/dt would be flux or flow.  So whenever the      <
flux or flow is called for in this theory, that is what you must        <
use.  If you insert anything else, as you want to do, you will          <
of course get nonsense.                                                 <

Bryant, I do not know what to say in this case. The problem is not
scientific - it is mythological, like many others in thermodynamics.
You know quite well (any student knows) that

T(dSi/dt)  =  AJ                                   /1/

is derived on the strict assumption that J is the reaction rate, v.
Now if some supreme mind, in order to obtain some valuable result, has
temporarily replaced v with dC/dt, we can only wonder why this
substitution has left /1/ correct. Nobody can know that.
Still there is a straightforward analogy. Just imagine that, in order
to obtain some valuable result, I replace J in Fick's first law

J = -D(dC/dx)                                    /2/

with dC/dt. You would explain in anger that dC/dt is given by Fick's
second law, would advise me to do my reading first etc. etc. I really
do not know what to say.

Best regards,
Pentcho

```