I'm already aware of the work by Raichle and colleagues about the default mode network and the associated energy consumption during the resting state. But I want to learn more about how much more energy the brain consumes during arduous thinking.
I also found already the paper by Lennie (2003) - The cost of cortical computing. This interesting work is a theoretical calculation based on knowledge about the metabolism of neurons. However, I still miss empirical work about this question.