A capacitor with capacitance \(C\) is charged to a potential difference \(V_0\), and a second capacitor with capacitance \(2C\) is charged to a potential difference \(2V_0\). The two charged capacitors are disconnected from their charging sources and connected to each other in parallel with plates of like polarity joined together. How much electrical energy is dissipated as thermal energy during the charge redistribution process after the system reaches a steady state?