AI Accelerator Efficiency & Physics of Computing
Koomey Compute TOPS/W & Landauer Limit Formula
Calculate AI Accelerator Compute Efficiency (TOPS/W), Energy per Operation (pJ/op), Rolf Landauer’s Minimum Irreversible Bit-Erasure Energy k_B * T * LN(2) in zeptojoules, and Headroom Factor Above Landauer.
Benchmark AI accelerator TOPS/W and picojoules/MAC against Landauer’s k_B*T*ln(2) floor!
Jonathan Koomey et al. (2011, IEEE Annals of the History of Computing) documented that computations per joule of dissipated electrical energy doubled roughly every 1.57–2.6 years across decades of silicon scaling—measured in modern AI accelerators as Tera-Operations per Second per Watt (TOPS/W = Throughput_TOPS / Power_W), whose exact reciprocal is Picojoules per Operation E_op_pJ = Power_W / Throughput_TOPS (since 1 W / 10^12 ops/s = 10^-12 J/op = 1 pJ/op = 10^9 zeptojoules)! Fundamentally, Rolf Landauer (1961, IBM Journal of Research and Development) proved from the Second Law of Thermodynamics that erasing ONE irreversible classical bit at absolute temperature T (Kelvin) MUST dissipate at least E_Landauer = k_B * T * LN(2) = 0.01380649 * T * LN(2) zeptojoules (1 zJ = 10^-21 J)—giving 2.8710 zJ/bit at 300 K room temperature!
Verify on Accelerator_TDP = 500 W (B2), INT8_Throughput = 2,000 TOPS (B3), Junction_Temp T = 300 K (B4), and Irreversible_Bits_Per_Op = 1,000 bit erasures (B5): Compute Efficiency is 2,000 / 500 = 4.00 TOPS/W (E2); Energy per Operation is 500 / 2,000 = 0.2500 pJ/op (250,000,000 zJ/op, E3); Landauer Single-Bit Minimum at 300 K is 2.8710 zJ (E4); and Thermodynamic Headroom Multiple (E3 * 10^9) / (B5 * E4) is 250,000,000 / 2,871 = 87,078x above the Landauer floor (E5)!
| Physics of Compute Metric (500W, 2,000 TOPS, T = 300 K, 1,000 Bits/Op) | Formula | Verified Output |
|---|---|---|
| Compute Efficiency (TOPS / W) | Throughput_TOPS / Power_W | 4.00 TOPS/W (20.00 @ 10k TOPS) |
| Energy per Operation (pJ / op) | Power_W / Throughput_TOPS | 0.2500 pJ/op (2.5e8 zJ/op) |
| Landauer Minimum per Bit (zJ) | 0.01380649 * T_Kelvin * LN(2) | 2.8710 zJ (0.7369 zJ @ 77 K LN2) |
| Multiple Above Landauer Bound | (E_op_pJ * 10^9) / (Bits_Op * E_Land_zJ) | 87,078x Irreversible Headroom |
Landauer Irreversible Bit-Erasure Energy Formula (in Zeptojoules)
Working in zeptojoules (1 zJ = 10^-21 J, so Boltzmann k_B = 0.01380649 zJ/K) keeps spreadsheet numbers human-readable without tiny scientific-notation exponents, while guarding T_Kelvin > 0 (Third Law of Thermodynamics)!
=LET(pw_w, B2, tp_s, B3, tm_k, B4, bt_o, B5, IF(OR(pw_w <= 0, tp_s <= 0, tm_k <= 0, bt_o < 1), "Invalid Thermodynamic Input", ROUND(0.01380649 * tm_k * LN(2), 4)))Cryogenic 77 K Liquid-Nitrogen & Next-Gen 10,000 TOPS Check
Cool the junction to liquid nitrogen T = 77 K in cell B4: Landauer’s floor drops nearly 4x to 0.7369 zJ/bit! Scale throughput 5x to 10,000 TOPS at 500 W: E_op falls to 0.0500 pJ/op (20.00 TOPS/W)!
=IF(ISTEXT(E4), E4, ROUND((E3 * 1000000000) / (B5 * E4), 0))Try the example
Use the original values or change them to test your understanding.