Definition - Landauer Principle

Overview

Landauer’s Principle establishes that erasing one bit of information must dissipate at least $k_{B}T\ln 2$ of energy as heat into the environment. This fundamental result bridges information theory and thermodynamics, proving that information processing has irreducible physical costs.

Source

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Key Concept

The minimum energy required to erase one bit of information:

$E_{min}=k_{B}T\ln 2$

Where:

• $k_B$ = Boltzmann’s constant ($1.38\times 10^{-23}$ J/K)
• $T$ = temperature in Kelvin
• $\ln 2\approx 0.693$

At room temperature (300K), this equals approximately $2.85\times 10^{-21}$ joules per bit erased.

Details

Why Erasure Costs Energy

When you delete information, you’re:

1. Reducing entropy of the data storage system
2. Increasing entropy of the environment by at least the same amount
3. This is thermodynamically analogous to isothermal compression

The second law of thermodynamics requires that total entropy cannot decrease, so the environment must absorb the “disorder” removed from the information system.

Information is Physical

Landauer’s principle proves that:

• Information isn’t just abstract—it has physical consequences
• Computation has fundamental thermodynamic limits
• There’s an irreducible energy cost to irreversible operations

Experimental Verification

Recent experiments have verified Landauer’s principle in:

• Single-bit memory systems
• Quantum many-body systems
• Nanoscale electronic devices

The principle applies to quantum systems too, where generalized entropy production tracks changes in information-theoretic quantities.

Implications

1. Ultimate Computer Efficiency: Sets minimum power consumption for irreversible computation
2. Reversible Computing: Reversible operations can theoretically avoid this cost
3. Maxwell’s Demon: Resolves the paradox—the demon must erase information
4. Thermodynamic Computing: Links computation to physical energy budgets

Connection to Computational Limits

Combined with the Bekenstein bound, Landauer’s principle:

• Sets ultimate limits on information density
• Constrains quantum computing possibilities
• Shows computation is fundamentally a physical process

Bridge Principle

Landauer’s principle connects Shannon’s abstract information theory to concrete thermodynamics, proving that bits are physical objects with real energy costs.

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Appendix

Created: 2024-12-31 | Modified: 2024-12-31

See Also

• Definition - Information Theory
• Definition - Bekenstein Bound
• Definition - Margolus-Levitin Theorem
• Black Hole Thermodynamics

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