Stopping such transmissions was one of the goals of the Tempest regulations promulgated by the government.
Tanenbaum, in one of his classic textbooks, has a brief section on how a rogue application could transmit data by modulating its cpu usage, so that noise, power usage, and other externally observable aspects of the system could be monitored for information sent by the application. Even though such transmissions would be noisy, that could be overcome by using forward error correction.