Landauer's Principle

Erasing Information Costs Energy

Information is not abstract. It is not mathematical fiction. It is stored in physical systems — in the magnetization of a hard drive, the charge of a capacitor, the spin of an electron. Because information is physical, manipulating it has physical consequences.

Landauer's principle, stated by Rolf Landauer in 1961, is the most precise and profound statement of the relationship between information and thermodynamics:

Erasing one bit of information requires dissipating at least k_BT ln 2 of energy as heat.

That's the principle. Simple. Let's unpack it.

What Erasure Means

Erasure doesn't mean deleting a file. It means resetting a physical system to a known reference state regardless of its previous state. If you have a bit — a magnetic domain, a charged capacitor — that might be 0 or 1, and you reset it to 0, you are erasing information.

Before the reset, the system was in one of two distinguishable states. After, it's in exactly one. The number of accessible microstates decreases. The entropy decreases. And by the Second Law, something else must increase to compensate. That something else is heat. The environment absorbs at least k_BT ln 2 per bit erased.

Why ln 2

A bit has two states. If you erased a system with N possible states to a single reference state, the entropy change would be k_B ln N. For a bit, N = 2, so ΔS = k_B ln 2. The energy dissipated is Q = TΔS = k_BT ln 2.

This is a lower bound. Real computers dissipate far more — sometimes a billion times more. But the limit is fundamental. Not an engineering problem. A law of physics.

Reversible Computation

Here's the remarkable corollary: computation that does not erase information can, in principle, be done reversibly with zero energy dissipation. If every logical operation can be reversed, no information is destroyed, no entropy is produced, no heat need be dissipated. This is the basis of reversible computing.

In practice, it's extraordinarily difficult. Every operation in a real computer eventually leads to information erasure — registers are reused, intermediate results discarded. But a fully reversible computer could compute forever without dissipating a single joule.

The Physicality of Information

Landauer's principle establishes that information is entropy. When you erase a bit, you increase the environment's entropy by exactly k_B ln 2. Information is entropy, and entropy is thermodynamics.

For most of the twentieth century, information theory and thermodynamics were separate fields — Claude Shannon working with bits and Clausius working with heat engines. Landauer showed they are the same field.

Computing's Heat Wall

At room temperature, k_BT ln 2 ≈ 2.9 × 10⁻²¹ joules. Tiny, but not zero. As transistors shrink, the energy per operation approaches this limit.

The limit extends to black hole thermodynamics. If information is physical, then information stored on a black hole's event horizon has thermodynamic consequences. The Bekenstein-Hawking entropy counts a black hole's information content. Landauer's principle connects them.

Why This Matters

Landauer's principle is about the fundamental relationship between knowledge and the physical world. To know something is to have information. To forget something is to erase information. And erasing costs energy.

The universe keeps a ledger. Every bit stored is a debt. Every bit erased is a payment. The interest rate is k_BT ln 2 per bit, forever.

The demon in Maxwell's thought experiment pays this price. Every computer pays this price. The price is universal.

Trolla out.