Information Landauer Bound Landauer From Ledger

The declaration's scope

Landauer's principle, proposed by Rolf Landauer in 1961, sets a lower bound on the energy a computer must dissipate to erase one bit of information: at least k_B T ln(2), where k_B is the Boltzmann constant and T is the temperature. At room temperature (300 K), this works out to about 2.87 × 10⁻²¹ joules. The principle is a key part of the thermodynamics of information, and experiments by Bérut et al. (2012) and others have verified it directly.

The Recognition Science library, a machine-checked collection of formal theorems, contains a declaration named landauer_from_ledger. In plain language, the declaration states that erasing entries from a ledger, a discrete record of events, has a minimum cost, and it identifies that cost with the thermodynamic bound. The declaration is a theorem in the library's own terms: it is tagged as proved, and its statement is the claim that the minimum erasure cost equals k_B T ln(2).

What the declaration does not do is prove the physics. The theorem's proof in the library is a placeholder, marked with the trivial proof of the proposition True. It does not derive the Landauer bound from first principles, nor does it connect the ledger abstraction to a physical system. The declaration is a formal statement of intent, not a derivation. The library also defines related quantities, such as the minimum erasure power (the Landauer energy divided by a fundamental timescale τ₀), but these are definitions, not theorems.

In Recognition Science, the declaration is part of a broader program that models information as physical reality. The library includes statements that information is physical and that quantum measurement is irreversible and costs energy. These are tagged as theorems in the library, but their proofs are also placeholders. The declaration landauer_from_ledger is best understood as a formal articulation of a target: it says what the framework aims to derive, not what it has already derived.

/-- In RS, Landauer's principle is about **ledger accounting**:
    
    1. Information = ledger entries
    2. Erasing = removing an entry
    3. Ledger must balance → cost to remove
    4. Minimum cost = thermodynamic limit
    
    The Landauer bound is the "transaction fee" for information deletion. -/
theorem landauer_from_ledger :
    -- Erasing ledger entries has minimum cost
    -- This is the thermodynamic bound
    True := trivial

/-- In RS, Landauer's principle is about **ledger accounting**:
    
    1. Information = ledger entries
    2. Erasing = removing an entry
    3. Ledger must balance → cost to remove
    4. Minimum cost = thermodynamic limit
    
    The Landauer bound is the "transaction fee" for information deletion. -/
theorem landauer_from_ledger :
    -- Erasing ledger entries has minimum cost
    -- This is the thermodynamic bound
    True := trivial

/-- **THEOREM**: At 300K, Landauer energy ≈ 2.87 × 10⁻²¹ J. -/
theorem landauer_room_temp_value :
    -- k_B × 300 × ln(2) ≈ 2.87 × 10⁻²¹ J
    True := trivial

What this page does not claim

The declaration does not prove that the Landauer bound holds for any physical system. The declaration does not derive the Landauer bound from the recognition cost function J. The declaration does not establish that information is physical; that is a separate, also unproved, statement in the library.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Information/LandauerBound.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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