Electrical circuit elements entropy production

The irreversible conversion of electrical energy into heat in electrical circuit elements, such as resistors, capacitors and inductances also leads to entropy production. The thermodynamic formalism of circuit elements can be developed by considering the changes in the energies associated with them. Section 10.1 showed that in the presence of a field we have... 

The first term is the entropy production due to chemical reactions, which can be dropped when considering only electrical circuit elements. For a resistor and a capacitor, (()> j — ( )2) in the second term may be identified as the voltage Vacross the element and dQ/dt as the electric current 7. If R is the resistance, according to Ohm s law, the voltage across the resistor = (cj) 1 — 4>2) = IF The entropy production is... 

In the previous section we have seen that the entropy production for electrical circuit elements is given by Td S/dt — VI in which V is the voltage across the... 

Example 3.20 Minimum entropy production in electrical circuits Determine the conditions that minimize the entropy generation in electrical circuits with n elements connected in series. Assume that the voltage drop across the circuit is kept constant. 

Therefore, in a circuit element, the entropy production is minimized if the current through the n elements is the same. In an electrical circuit, the relaxation to the stationary state is very fast, and nonuniform values of/are not observed. 

Thus, in a circuit element, the entropy production is minimized when the current is uniform along the circuit. (Feynman [5] indicates he has observed this relation between entropy production and uniformity of electric current.) In the analysis of electrical circuits, the condition that the current should be uniform is usually imposed on the system because we do not observe any charge accumulation in any part of the system. In electrical systems the relaxation to the stationary state of uniform I is extremely rapid, hence non-uniform or discontinuous I are not observed. 

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