Abstract Common Mistakes in Watch out! Most adiabatic logic families - PDF document

Abstract Common Mistakes in Watch out! Most “adiabatic” logic families are not what I call truly adiabatic. Adiabatic Logic Design • – Many don’t satisfy the general definition of an adiabatic process in physics. – Many “adiabatic” logic families aren’t even asymptotically adiabatic! and – I give my definition of “true adiabaticity.” • Yet, true adiabatic design will be required for most 21 st -century computing! How to Avoid Them – At the nanoscale, energy dissipation is by far the dominant limiting factor on computing system performance, esp. for tightly-coupled parallel computations. – Truly-adiabatic design is the only way to work around the fundamental Michael P. Frank thermodynamic limits on computing which are rapidly being approached. University of Florida • Some of the most common adiabatic design mistakes, and their solutions: College of Engineering – Use of fundamentally non-adiabatic components, such as diodes. Departments of CISE and ECE – Turning off transistors while there is nonzero current through them! mpf@cise.ufl.edu – Overly-constrained design style that imposes a limited degree of logical reversibility and/or asymptotic efficiency. • Overview of some recent advances in adiabatic circuits at UF: Methodologies in Low Power Design Workshop – 2LAL (a simple 2-level adiabatic logic) Int’l Conf. on Embedded Systems and Applications – GCAL (General CMOS Adiabatic logic) Int’l Multiconf. In Computer Sci. & Computer Eng. – High- Q MEMS/NEMS based resonant power supplies Las Vegas, Nevada, June 23-26, 2003 – Analysis of cost-efficiency benefits of adiabatics, & FET energy-dissipation limits Organization of Talk 1. Why adiabatic design? • Moore’s Law vs. Fundamental Limits of Computing Moore’s Law vs. the Fundamental 2. What does “adiabatic” mean, anyway? • Original, literal meaning vs. modern meaning Physical Limits of Computing 3. Adiabatic Circuits & Reversible Computing • Dispelling the Misconceptions 4. Common Mistakes to Avoid in Adiabatics • Overview of adiabatic design rules 5. Example adiabatic circuit styles: • SCRL, 2LAL 6. Other recent advances: • NEMS resonators, FET entropy-generation limits 7. Conclusions ITRS Feature Size Projections Moore’s Law – Devices per IC 1000 Bacterium 1,000,000,000 Madison uP chan L Itanium 2 DRAM 1/2 p 100,000,000 P4 min Tox Intel µpu’s P3 max Tox 10,000,000 100 Virus P2 486DX Feature Size (nanometers) Pentium 1,000,000 386 286 100,000 Protein 10 8086 molecule 10,000 4004 Avg. increase 1,000 Early of 57%/year DNA molecule 1 thickness 100 Fairchild 10 ICs Atom 0.1 1 1995 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 1950 1960 1970 1980 1990 2000 2010 Year of First Product Shipment We are here 1

✄ ✁ � ☎ ✄ ✄ ✂ Trend of minimum transistor switching energy Fundamental Physical Limits of Computing Min transistor switching energy, kTs (½ CV 2 gate energy calculated from ITRS ’99 geometry/voltage data) 1000000 Implied Affected Quantities in Thoroughly Universal Facts Information Processing High Confirmed 100000 Physical Theories Speed-of-Light Communications Latency Low 10000 Limit Theory of Uncertainty Information Capacity 1000 Principle trend Relativity Information Bandwidth Definition 100 of Energy Memory Access Times Quantum Reversibility 10 2 nd Law of Theory Processing Rate Thermodynamics 1 1995 2005 2015 2025 2035 Adiabatic Theorem Energy Loss Year of First Product Shipment per Operation Gravity Landauer’s 1961 principle from basic quantum theory What is entropy? Before bit erasure: After bit erasure: • First was characterized by Rudolph Clausius in 1850. 0 0 s 0 s 0 N – Originally was just defined as heat ÷temperature . … … … distinct – Noted to never decrease in thermodynamic processes. states – Significance and physical meaning were mysterious. 0 0 s N −1 s N −1 2 N Unitary • In ~1880’s, Ludwig Boltzmann proposed that entropy is distinct (1-1) just the logarithm of the number of states, S = k ln N states evolution – What we would now call the information capacity of a system 1 0 s s 0 N N – Holds for systems at equilibrium, in maximum-entropy state … … … distinct … • The modern consensus resulting from 20 th -century states physics is that entropy is simply the amount of unknown 1 0 s s N −1 2 N −1 or incompressible information in a physical system. – Contributions by von Neumann, Shannon, Jaynes, Zurek Increase in entropy: S = log 2 = k ln 2. Energy lost to heat: ST = kT ln 2 Adiabatic Cost-Efficiency Benefits 1.00E+33 operations per US dollar -operations per US dollar Scenario: $1,000/3-years, 1.00E+32 100-Watt conventional ~100,000× 1.00E+31 computer, vs. reversible What is “adiabatic?” g n 1.00E+30 computers w. same capacity. i t u p m g n o i t 1.00E+29 c u e p ~1,000× l m b o i s c r 1.00E+28 e e v b l e i r s r Evolution of the term e e Conventional irreversible computing s 1.00E+27 v a e c r - e t s s e a B c 1.00E+26 - t s r o W 1.00E+25 All curves would 0 1.00E+24 if leakage not reduced. Bit- 1.00E+23 Bit 1.00E+22 2000 2010 2020 2030 2040 2050 2060 2

The Carnot Cycle Steps of Carnot Cycle P • Isothermal expansion at T H • In 1822-24, Sadi Carnot analyzed the efficiency • Adiabatic (without flow of of an ideal heat engine all of whose steps were T H heat) expansion T H → T L reversible , and furthermore proved that: • Isothermal compression at T L – Any reversible engine (regardless of details) would T L have the same efficiency ( T H − T L )/ T H . • Adiabatic compression T L → T H V – No engine could have greater efficiency than a reversible engine w/o producing work from nothing – Temperature itself could be defined on a thermodynamic scale based on heat recoverable by a Adia- Iso- batic Iso- thermal reversible engine operating between T H and T L Adia- thermal batic Reser- Reser- Reser- Reser- voir voir voir voir Carnot Cycle Terminology Old and New “Adiabatic” • Adiabatic (Latin): literally “Without flow of heat” • Consider a closed system where you just – I.e. , no entropy enters or leaves the system lose track of its detailed evolution: • Isothermal : “At the same temperature” – It’s adiabatic (no net heat flow), – Temperature of system remains constant as entropy enters or leaves. – But it’s not “adiabatic” (not isentropic) • Both kinds of steps, in the case of the Carnot cycle, are “The System” • Consider a box containing some heat, examples of isentropic processes flying ballistically out of the system: – “at the same entropy” – It’s not adiabatic , (no heat flow) – I.e. , no (known) information is transformed into entropy in Box o’ Heat • because heat is “flowing” out of the system either process – But it’s “adiabatic” (no entropy is generated) • But, the usage of the word “adiabatic” in applied physics has mutated to essentially mean isentropic. Quasi-Adiabatic Justifying the Modern Usage • Complete adiabaticity means absolutely zero rate of entropy generation • In an adiabatic process following a desired – Requires infinite degree of isolation of system from trajectory through configuration space, uncontrolled external environment! – No heat flows in or out of the subsystem consisting of – ∴ Impossible to completely achieve in practice. those particular degrees of freedom whose variation carries out the motion along the desired trajectory. • Real processes are only adiabatic to the extent • E.g. , the computational degrees of freedom in a that their entropy generation approaches zero. computational process. – Term “quasi-adiabatic” emphasizes imperfection – No heat flow � no entropy flow • Asymptotically adiabatic designs conceptually • Heat is just energy whose configuration info. is entropy approach 0 in the limit of variation of specified – No entropy flow � no sustained entropy generation technology design parameter(s) • Since bounded systems have a maximum entropy – E.g. , low device frequency, large device size 3