Entropy balance of a thermostatted resistor (${\dot{S}}_{\mathrm{tot}}=I^{2}R/T$)

A resistor at fixed temperature and unchanged thermodynamic state has no net entropy accumulation. Electrical work becomes heat at rate $I^{2}R$, which is exported to the thermostat. In the ideal work-source model the surroundings gain entropy at rate $I^{2}R/T$, equal to the total entropy production. Additional losses inside a real power source add to this idealized budget.