Information is Physical

Landauer's principle: the mean heat cost of cyclic bit reset

LANDAUER'S PRINCIPLE (1961)

Mean heat ≥ kT ln(2) per unbiased bit reset

For cyclic reset of an initially unbiased bit in a degenerate memory coupled to an isothermal bath at T, the minimum mean heat delivered to the bath is kT ln(2), about 2.87 × 10⁻²¹ J at 300 K. Here k is Boltzmann's constant. A biased bit has uncertainty H(p), giving kT H(p) under the same assumptions; a known bit has no uncertainty to erase. Correlations and memory energy differences require their own accounting.

BIT ERASURE DEMONSTRATION

Each reset illustrates a newly prepared unbiased bit; the counter tracks its minimum mean heat.

Bits Erased 0

Minimum Mean Heat 0

At 300 K 0 J

REVERSIBLE vs IRREVERSIBLE COMPUTATION

IRREVERSIBLE (AND gate)

2 bits in → 1 bit out

Many-to-one logical mapping.
Reset cost depends on input uncertainty.

REVERSIBLE (Toffoli gate)

3 bits in → 3 bits out

Logical information preserved.
No logical-erasure minimum; hardware can dissipate.

IMPLICATIONS

• Reset cost follows uncertainty: reading, writing and logical operations have no universal positive erasure cost.
• Information has a physical substrate, with physical constraints.
• Cyclic demons require memory accounting: restoring uncertain memory contributes to the full thermodynamic balance.
• Reversible logic preserves information; practical energy use depends on the hardware and protocol.

Information is physical. — Rolf Landauer

Landauer's bound connects a specified memory reset to thermodynamics. It supplies no universal energy price for a thought or logical operation.

core conceptinformationheat · erasure cost