The Thermodynamics of Brains and Computers

The question of how much energy is needed to carry out a computation can be traced back to a thought experiment of Maxwell (of the Maxwell equations), now called Maxwell's demon. This was an ingenious idea to explore whether the second law of thermodynamics, that entropy always had to increase, could be violated by a tiny creature (or microscopic apparatus) that could open or close a tiny molecule-size door in a wall that would let only high-energy molecules pass through the door, thus causing the transfer of heat from a cold to hot region. Physicists like Leo Szilard, Leon Brillouin, Rolf Landauer, and Charles Bennett thought deeply about whether a demon could exist and came up with the conclusion that the energy needed to carry out a computation could be made arbitrarily small (smaller than the thermal energy kT) but only for some fixed amount of time. Experimentalists like Mark Raizen at Georgia Tech have actually built working nano-size demons but the demons were not able to violate the second law of thermodynamics.

To give you some perspective on these issues, let's compare a biological computer like an adult human brain (see upper left image) with the Summit supercomputer (see upper right image) which, as of 2019, is one of the most powerful supercomputers in the world. Although it is difficult to compare brains with digital silicon-based computers since we don't yet know the principles of how brains process information, a rough estimate based on the number of digital electrical pulses (action potentials) that the approximately 10¹¹ neurons in a human brain send to one another per second via approximately 10¹⁴ contacts (synapses) suggests that an adult human brain carries out about (10¹⁸) logical operations per second (an exaflop) which is about the capability of the Summit supercomputer. So you are living during an interesting time when digital computers are starting to attain the raw computational capability of an adult human brain.

Although a human brain and and the Summit computer are believed to be roughly comparable in computational power, they differ enormously in terms of their thermodynamic properties. The Summit computer occupies about two tennis courts of floor space, consumes about 15,000,000 watts, requires a large intricate cooling system (hidden under the floor) to dissipate the resulting heat, and is utterly non-portable. A human brain is about the size of your two fists, consumes about 15 watts (even when you are solving a hard physics problem), and is completely practical to carry around since it has a mass of about 1.5 kg. (It is also worth pointing out that brains, unlike computers, self-assemble themselves and are also able to program themselves.)

So brains are impressive compared to the best supercomputers in terms of computational capability per unit volume per unit power. But for physicists, it is interesting ask an additional question: although brains are impressive compared to computers, are they impressive in some absolute physical sense? That is, has evolution led to brains that are close to optimal in that no other physical system that operates at room temperature and that consumes 15 watts can achieve a exaflop of computation or more? The answer is not known and is being studied by a variety of physicists, engineers, computer scientists, and biologists.