Information Landauer Bound Landauer Room Temp Value

Room temperature erasure

Landauer's principle, proposed by Rolf Landauer in 1961, states that erasing one bit of information must dissipate at least k_B T ln(2) joules of heat, where k_B is the Boltzmann constant and T is the temperature of the environment. This is not a statement about the speed of a computer or the cleverness of its design; it is a thermodynamic floor. At room temperature, conventionally taken as 300 kelvin, that floor works out to approximately 2.87 x 10^-21 joules per erased bit.

The value is small but not abstract. A modern computer chip performing a bit operation dissipates around 10^-15 joules, which is roughly a million times above the Landauer limit. The gap defines an engineering target: in principle, a machine that operates reversibly, never erasing information, could approach zero dissipation. Experiments have confirmed the principle directly, beginning with Bérut et al. in 2012, followed by feedback-controlled erasure in 2014 and a single-atom demonstration in 2016; the best current experiments sit about ten times above the limit.

The machine-checked library of formal statements in Recognition Science (RS) defines the room-temperature value as a named declaration, landauer_room_temp_value. The declaration states that k_B times 300 times ln(2) is approximately 2.87 x 10^-21 joules. It also defines the supporting pieces: the Boltzmann constant as 1.380649 x 10^-23, room temperature as 300 kelvin, and the energy function landauerEnergy T as k_B times T times ln(2). The declaration is a definitional checkpoint, not a derivation: it pins down the numerical value that the framework's other statements refer to.

In RS, the Landauer bound connects to the framework's own timescale, called tau0, which sets a fundamental recognition rate. The framework models erasure as a recognition event followed by forgetting, and it defines a minimum erasure power as the Landauer energy divided by tau0. A statement in the library, landauer_from_tau0, asserts that erasing at a rate of one over tau0 requires power at least k_B T ln(2) divided by tau0. This is a formal statement within the framework; it does not by itself prove that real physical erasure must obey this rate.

The declaration does not claim to derive the Landauer bound from first principles. The bound itself is a classical result from thermodynamics, and the framework's library reproduces it as a definitional consequence, not as a new physical law. The statement jcost_equals_thermodynamic, which states that the J-cost framework reproduces thermodynamics, is a placeholder whose proof is the trivial statement True, not a substantive derivation. The value 2.87 x 10^-21 joules is a numerical restatement of a known formula, not an independent prediction.

What the declaration does establish is a fixed reference point. When the framework's library speaks of efficiency ratios, minimum erasure power, or the gap between current computers and the thermodynamic limit, it uses this room-temperature value as the baseline. The practical consequence is clear: the number gives engineers and theorists a concrete target for ultra-low-power computing, and it frames the framework's claim that information is physical, since erasing it must always cost energy.

/-- The Landauer energy at room temperature.
    E = k_B × T × ln(2) ≈ 2.87 × 10⁻²¹ J ≈ 0.018 eV -/
noncomputable def landauerEnergy (T : ℝ) : ℝ := k_B * T * Real.log 2

/-- **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

/-- Current computer energy per bit operation (for comparison).
    Modern CMOS: ~10⁻¹⁵ J per bit operation
    Landauer limit: ~10⁻²¹ J per bit operation
    Ratio: ~10⁶ (a million times above limit!) -/
noncomputable def currentComputerEnergy : ℝ := 1e-15  -- J per bit op

/-- Landauer's principle has been experimentally verified:
    - Bérut et al. (2012): Erasure in optical trap
    - Jun et al. (2014): Feedback cooling experiments
    - Verified to within a factor of ~10 of the limit -/
def experimentalVerification : List String := [
  "Bérut et al. (2012): First experimental verification",
  "Jun et al. (2014): Feedback-controlled erasure",
  "Hong et al. (2016): Single-atom demonstration",
  "Current best: ~10× Landauer limit"
]

/-- **THEOREM**: The J-cost of erasure equals the thermodynamic cost.
    J_erase ∝ ln(2) (the information content of 1 bit) -/
theorem jcost_equals_thermodynamic :
    -- The J-cost framework reproduces thermodynamics
    True := trivial

What this page does not claim

The declaration does not derive the Landauer bound from the framework's axioms; it restates a known thermodynamic formula. The statement jcost_equals_thermodynamic does not contain a substantive proof that the J-cost framework reproduces thermodynamics. The room-temperature value is not an independent prediction; it is a definitional evaluation of a classical formula.

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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