Landauer Limit & Chip Quantization Thermodynamic Simulator

Silicon Nanometer Gate Switching Array (2nm GAA Topology)

60 FPS

Direct Action: Click / Drag across gates to force bit flips & trigger heat vectors

Operating Energy per Bit 1.25e-18 J 1.25 aJ / bit flip

Landauer Theoretical Limit 2.87e-21 J E = kB · T · ln(2) at 300K

Thermodynamic Overhead Factor 435.5x Dissipation ratio vs physical min

Total Thermal Power 12.50 W EDP: 3.12e-28 J·s

Physical Principles & Dynamic Phase Contraction

In 1961, Rolf Landauer demonstrated that erasing or changing one bit of information in a non-reversible system fundamentally dissipates a minimum entropy quantity of energy:

E_min = k_B · T · ln(2)

In deep-submicron process nodes (such as 2nm Gate-All-Around field effect transistors), standard FP16 operations discard high amounts of intermediate bit states, creating massive thermal dissipation. By quantizing down to INT8 or INT4, or leveraging Reversible Phase Contraction (where microstates are topologically preserved without information loss), total switching dissipation dramatically approaches the fundamental Landauer limit.

Preset Experiment Profiles

Silicon Telemetry Deck

Quantization Precision

FP16

INT8

INT4

Reversible

Operating Voltage (Vd) 0.70 V

Die Temperature (K) 300 K

Clock Frequency (f) 2.50 GHz

Signal-to-Noise Ratio 34.2 dB

Bandwidth Reduction 50.0%

Temperature, voltage and clock in the source energy model

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Read the explanation

Use the native INT8 source mode at zero point seven volts. Start at three hundred kelvin, then move the temperature slider to one hundred fifty kelvin. The source computes the Landauer bound as Boltzmann constant times temperature times natural logarithm of two. With its configured Boltzmann constant, the displayed bound falls from approximately two point eight seven one zeptojoules to one point four three five zeptojoules. Both exact held bars use one hundred forty pixels per zeptojoule. This temperature action does not change the source assigned switching energy, six hundred twelve point five attojoules. Notice that zeptojoules and attojoules are different units. The assigned energy to bound ratio therefore doubles. The bound concerns ideal information erasure; it does not certify the source chip labels or make its assumed switching energy a measured hardware result. Reset to the native baseline preset, INT8 mode and three hundred kelvin. Change only the voltage slider from zero point seven to zero point three five volts. The source assigned switching model is one half capacitance times voltage squared. Its baseline capacitance is two point five femtofarads, and the INT8 mode multiplier is one. Halving voltage quarters voltage squared. The assigned energy therefore falls from six hundred twelve point five attojoules to one hundred fifty three point one two five attojoules. Both held bars use zero point seven pixels per attojoule. Temperature is unchanged, so the separately computed Landauer bound remains approximately two point eight seven one zeptojoules. These exact numerical results follow the stated source model assumptions. They are not measurements of a real fabrication process, nor universal energy savings for a numeric format. Reset again to the baseline source parameters. Hold voltage, temperature and INT8 mode fixed, then double the native clock slider from two point five to five gigahertz. The source assumes two hundred billion bit operations per second at the baseline INT8 setting, proportional to clock frequency. Its assigned per operation energy remains six hundred twelve point five attojoules. Multiplying energy by assigned operations per second makes the computed power double, from zero point one two two five to zero point two four five milliwatts. Meanwhile energy delay product is energy divided by clock frequency, so it halves from two point four five to one point two two five times ten to the negative twenty five joule seconds. The two bar rows use explicitly separate units and fixed scales. This comparison explains the source formulas, not actual device timing, calibrated thermal performance, signal to noise, or the physical validity of its reversible mode assumptions.