Thermodynamics of Irreversible Process

Tools

`landauer_heat`

Compute the minimum Landauer heat for an irreversible operation. Given the number of bits erased (or paths folded), returns Q = N * kT * ln(2) in joules at the specified temperature, plus the Bule equ...

`first_law_frf`

Apply the first law of fork/race/fold: H_fork = I_fold + H_vent. Given the forked entropy (number of parallel paths), compute the information preserved by the fold and the entropy vented. Returns the ...

`free_energy_budget`

Given a computation with known topology (beta_1 collapse depth, number of folds, number of vents), compute the total free energy budget: minimum energy to complete, energy per fold, energy per vent, a...

`inference_cooling`

Model inference as refrigeration. Given a model with N parameters, K active experts, and token budget T, compute: thermodynamic cost per inference step, the cooling cycle analogy (Bayesian=heat pump, ...

`entropy_partition`

Given a fork with N paths where a subset is selected, compute: information gained (log2(N) bits), information destroyed ((N-1)/N of input entropy), Landauer heat generated, and the void boundary compl...

`landauer_heat_sandwich`

Compute the Landauer heat sandwich: kT ln 2 per bit ≤ heat ≤ fork energy. Returns thermodynamic bounds and efficiency metrics.

`thm_landauer_equality_characterization`

Frontier entropy equals failure tax if and only if liveBranches ≤ 2; for n ≥ 3, entropy is strictly less than failure tax. This sharpens the paper: the failure-tax floor strictly dominates entropy for...

`thm_infinite_erasure`

For PMFs with genuinely infinite support (not Finset-coverable), the entropy-to-heat chain still holds because the chain only requires entropy positivity (≥ log 2 bits when ≥ 2 live branches), not fin...

`thm_data_processing_inequality`

Strict data processing inequality for finite PMFs: H(f(X)) ≤ H(X) for any function f, with strict inequality H(f(X)) < H(X) when f is non-injective on the support. Conditional entropy H(X\ [LEDGER: TH...

`thm_coarsening_thermodynamics`

Landauer heat of network coarsening and the thermodynamic arrow of abstraction. Every non-trivial coarsening (many-to-one quotient) erases information, incurring Landauer heat ≥ kT ln 2 × information ...

`thm_coarsened_beauty_floor`

For systems that arose from non-trivial coarsening: zero topological deficit is the strict unique global minimum for every strict generalized-convex cost and every strict real monotone objective, WITH...

`thm_entropic_refinement_calculus`

Conditional entropy as a functorial information measure on the category of quotient refinements. Identity law: H(X\ [LEDGER: THM-ENTROPIC-REFINEMENT-CALCULUS]

`thm_rate_distortion_frontier`

Rate-distortion frontier for network coarsening. Given a family of many-to-one quotients, there exists a minimum-rate member (minimum information erasure), a minimum-heat member (since heat = kT ln 2 ...

`thm_enriched_convergence`

Reduces the convergence schema from 7 axioms to 5 by deriving A6 (forkRaceFoldAttractor) and A7 (noAlternativeInModelClass) from throughput landscape optimization. The throughput-maximal skeleton has ...

`thm_fold_erasure`

Any fold on ≥ 2 branches with a non-injective merge erases information: `H(inputs \| output) > 0`. Composes `conditionalEntropyNats_pos_of_nonInjective` from the strict data processing inequality. [LE...

`thm_fold_heat`

Information erased by non-injective fold has Landauer heat cost `≥ kT ln 2 · H(inputs \| output) > 0`. Composes fold-erasure with the Landauer bridge. [LEDGER: THM-FOLD-HEAT]

`thm_erasure_coupling`

For systems where fold is many-to-one, construct a `ThermodynamicObservableCoupling` as a *theorem* (not axiom). Latency/waste floor maps derived from heat dissipation physics. The coupling is built f...

`thm_fold_injectivity_boundary`

Injective fold produces zero conditional entropy; the erasure coupling degenerates. This is the *exact boundary* of the erasure-sufficient regime: only injective folds (lossless merges) fall outside t...

`thm_vent_heat_is_one`

Vent heat is exactly one [LEDGER: THM-VENT-HEAT-IS-ONE]

`thm_sliver_is_heat`

Sliver is heat [LEDGER: THM-SLIVER-IS-HEAT]

`thm_heartbeat_self_sustaining`

The heartbeat loop vent→heat→sliver→positivity→race→losers→vent is self-sustaining [LEDGER: THM-HEARTBEAT-SELF-SUSTAINING]

`thm_sliver_from_vent`

Master theorem: sliver from vent [LEDGER: THM-SLIVER-FROM-VENT]

`thm_fold_heat_hierarchy`

Classification of folds by thermodynamic heat signature: injective = 0 heat, non-injective fibers generate strictly positive heat, uniform fold heat = kT ln2 × H(X\ [LEDGER: THM-FOLD-HEAT-HIERARCHY]