July 8, 2011
Our computers dissipate a lot of heat. The CPU of some computers will dissipate more that a hundred watts under peak conditions. According to data supplied by Intel, the Intel Pentium D Processor 960 has a peak power dissipation of 130 Watts. Does it really take that much power to do computation, or is all this heat just a reminder that we still don't know how to build efficient electronics?
That sounds like a problem for a physicist to tackle. Computer pioneer and physicist, John von Neumann, was the first to realize from entropy considerations that there must be a finite energy involved in computation, but it wasn't until 1961 that the problem was rigorously tackled by Rolf Landauer of IBM. Landauer reasoned that when a bit of information is irreversibly transformed, as in erasure, or when two bits combine logically to yield just a single bit from the two, some information is lost.
Since information and entropy are connected, it's possible to calculate the energy involved in the transformation of a single bit under ideal circumstances. This energy, EL, known as the Landauer limit is given as
EL = kT(ln2)
where k is the Boltzmann constant, T is the absolute temperature at which the computation takes place, and ln2 is the natural logarithm of two, or about 0.69315. At room temperature, 298.15 K, this calculates out to be just 0.0178 electron volt. For those whose minds aren't calibrated in eV, this is just 2.8519 x 10-21 joule.
Although the formal derivation of this formula is more involved, it's easy to see its logical basis. The Boltzmann entropy, S is given as
S = k(lnΩ)
where Ω is the the number of ways you can arrange items in a thermodynamic system. When talking about bits of information, there are just two states, thus the ln2 term. One of Maxwell's thermodynamic equations that I discussed in a previous article (Maxwell's Other Equations, April 6, 2011) relates a change in system energy, dU, to a change in entropy,
dU = TdS - PdV
Our computers are not usually subjected to a volume change, dV, so we can ignore the PdV term, where P is the pressure. Combining the equations gives us a reason to believe in the Landauer limit.
Since a watt is a joule/sec, we should be able to perform at least 1020 bit operations a second for just a watt expenditure. Compare this to the 9.89 megawatts it takes for the RIKEN K Computer to perform 8.2 petaflops; that is, 8.2 x 1015 floating point operations per seconds, as described in a previous article (Special K, June 23, 2011).
A floating point operation does take a few bit operations to perform, so to be generous, let's say that these 8.2 petaflops convert to 1020 bit operations per second, so our computing efficiency is about 0.00001%. We're obviously computing under the wrong paradigm!
One possible way to increase computational efficiency is to change our mindset from using electrons as current carriers to using electrons as magnets. I mentioned logic operations using the older magnetic bubble technology and the newer spintronic devices in a previous article (Spintronics, February 1, 2011). Electrical engineers at the University of California at Berkeley are doing just that in a study published in Physical Review Letters.[2-3]
The UC-Berkeley team, led by Jeffrey Bokor, Professor of Electrical Engineering and Computer Science and scientific director of the Molecular Foundry at Lawrence Berkeley National Laboratory, has created nanomagnetic logic structures that are near the Landauer limit. One caveat is that their computational speed, given by changes in driving magnetic fields, was slow. The slow speed is probably necessary since thermodynamics always requires equilibrium, or quasi-equilibrium, states.
The team built a majority logic gate from nanomagnets. In a majority logic gate, the output is determined by a majority "vote" of the inputs. In the example shown in the figure, there are three inputs and one output. Magnetic contrast imaging in the Advanced Light Source at Lawrence Berkeley National Laboratory shows nanomagnets with the north pole facing downwards as bright spots (also represented by the red bars), and nanomagnets with the north pole facing upwards as dark spots (represented by the blue bars). The output is the second bar from the right, and its state is determined by the surrounding bars (top, left and bottom).
The nanomagnets used in this demonstration device were about 100 nanometers wide and about 200 nanometers long. The demonstration logic cell actually used electrical currents to generate the magnetic fields that flipped the magnetic bits. Said Brian Lambson, one of the coauthors of this work, "We are working now with collaborators to figure out a way to put that energy in without using a magnetic field, which is very hard to do efficiently... A multiferroic material, for example, may be able to control magnetism directly with a voltage rather than an external magnetic field."
The work was supported by the National Science Foundation.
|A majority logic gate formed from six nanomagnets.|
The output reflects the majority vote of the three input.
See text for details.
- Rolf Landauer, "Irreversibility and heat generation in the computing process," IBM Journal of Research and Development, vol. 5, no. 3 (July 1961), pp. 183-191. A PDF image can be found here.
- Brian Lambson, David Carlton, and Jeffrey Bokor, "Exploring the Thermodynamic Limits of Computation in Integrated Systems: Magnetic Memory, Nanomagnetic Logic, and the Landauer Limit," Physical Review Letters, vol. 107, no. 1 (July 1, 2011), Document No. 010604.
- Robert Sanders, "Magnetic memory and logic could achieve ultimate energy efficiency," University of California - Berkeley Press Release, July 1, 2011.
- Rolf Landauer, "Dissipation in Computation," Physical Review Letters, vol. 53, no. 12 (September 17, 1984), p. 1205.
Permanent Link to this article
Linked Keywords: Computer; heat; central processing unit; CPU; watt; Intel Pentium D Processor 960; physicist; John von Neumann; entropy; energy; Rolf Landauer; IBM; bit; irreversible process; logic gate; information; Landauer limit; Boltzmann constant; absolute temperature; natural logarithm; Kelvin; K; electron volt; joule; Boltzmann entropy; thermodynamic system; Maxwell's thermodynamic equations; system energy; volume; pressure; RIKEN K Computer; petaflops; paradigm; electron; current carrier; electron magnetic dipole moment; magnet; magnetic bubble technology; spintronic; electrical engineer; University of California at Berkeley; Physical Review Letters; Jeffrey Bokor; Computer Science; Molecular Foundry; Lawrence Berkeley National Laboratory; majority function; majority logic gate; Advanced Light Source; National Science Foundation.
for your holiday gifts
Latest Books by Dev Gualtieri
Thanks to Cory Doctorow of BoingBoing for his favorable review of Secret Codes!
Blog Article Directory on a Single Page
- Verbal Cues and Stereotypes - December 8, 2016
- Capacitance Sensing - December 5, 2016
- Gallium Nitride Tribology - December 1, 2016
- Lunar Origin - November 27, 2016
- Pumpkin Propagation - November 24, 2016
- Math Anxiety - November 21, 2016
- Borophene - November 17, 2016
- Forced Innovation - November 14, 2016
- Combating Glare - November 10, 2016
- Solar Tilt and Planet Nine - November 7, 2016
- The Proton Size Problem - November 3, 2016
- Coffee Acoustics and Espresso Foam - October 31, 2016
- SnIP - An Inorganic Double Helix - October 27, 2016
- Seymour Papert (1928-2016) - October 24, 2016
- Mapping the Milky Way - October 20, 2016
- Electromagnetic Shielding - October 17, 2016
- The Lunacy of the Cows - October 13, 2016
- Random Coprimes and Pi - October 10, 2016
- James Cronin (1931-2016) - October 6, 2016
- The Ubiquitous Helix - October 3, 2016
- The Five-Second Rule - September 29, 2016
- Resistor Networks - September 26, 2016
- Brown Dwarfs - September 22, 2016
- Intrusion Rheology - September 19, 2016
- Falsifiability - September 15, 2016
- Fifth Force - September 12, 2016
- Renal Crystal Growth - September 8, 2016
- The Normality of Pi - September 5, 2016
- Metering Electrical Power - September 1, 2016
- Transitioning to Utopia - August 29, 2016
- The Cheerios effect - August 25, 2016
- It's the Humidity - August 22, 2016
- Clinging to Theory - August 18, 2016
- Circumscribing Semicircles with Triangles - August 15, 2016
- Insecticidal Sweeteners - August 11, 2016
- Coffee Break - August 8, 2016
- Darker Matter - August 4, 2016
- Ten Rules of Statistics - August 1, 2016
- Shampoo - July 28, 2016
- The Happiness Equation - July 25, 2016
- The Planck Constant and the Kilogram - July 21, 2016
- Mars Landing 1976 - July 18, 2016
- Cartograms - July 14, 2016
- Alvin Toffler - July 11, 2016
- Rare Earth Metals from Fly Ash - July 7, 2016
- Harvard Metamaterial Flat lens - July 4, 2016
- Visualization in Science and Math - June 30, 2016
- Planet Nine - June 27, 2016
- Casting Lots in the Digital Age - June 23, 2016
- High-Entropy Alloys - June 20, 2016
- George Westinghouse - June 16, 2016
- Humidity Sensing - June 13, 2016
- Stellar Classification - June 9, 2016
- The Square Root of Two - June 6, 2016
- Fluidized Beds - June 2, 2016
- Memorial Day, Solomon Golomb - May 30, 2016
- Christiaan Huygens' Coupled Pendulums - May 26, 2016
- Side-Channel Attacks - May 23, 2016
- Seven Important Chemical Separations - May 19, 2016
- Antennas - May 16, 2016
- Avoided Numbers - May 12, 2016
- Analogy and Scientific Thought - May 9, 2016
- Smectic Martensite - May 5, 2016
- The Nanoscale Shakes - May 2, 2016
Deep Archive 2006-2008