| physics is an approximationing method that calls formulation, "law", and-but, thereby, at arbitrary-precision, it fails the reasonable-doubt test, so, as it is-not absolute, its results may-be-retraceable revertibly recoverably of their origins... |
Computations in physics are oft done by matching asymptotic ends of 'abrupt' and 'adiabatic' functions, with transitional values estimated by 'ingenious' perturbation theory that assumes a compound 'superposition' of the many states already extant in each end...
Thermodynamics may,-be one of those multimodal functionalities, equivalent to the ends and means (transitionals) of 'crudely' natural-process-recoverable Gibbs, Free, energy, and-with, 'not-so-crudely' clever-process-recoverable Entropy, energy—like a 'soft-trapdoor' that readily yields a significant utilization that aboriginal mankind recognizes through experience, even sophistication, but, very-unreadily,-yields to a significant-computation-like-effort 'pushing the envelope' even comparable to exhaustive-decryption-think that modern university-level mankind recognizes...
(e.g.) "The Second Law of Thermodynamics"—sometimes applies only to the whole universe, sometimes to closed systems, and is stated variously, sometimes with Calories, sometimes with Entropy, and claims also-variously that heat flows in one direction, entropy is energy unavailable to do work, entropy is irreversible-disorder in a system... and so on—
A simple paradigm of entropy, popularized decades ago, is, a chamber of two halves, one containing gas, the other is vacuum, and, opening the halver-partition, allows the gas into both halves, and then-essentially can never revert to filling only one-half, nor the-other...
But, it-is an approximation, and, equally importantly, it-is, in most experiments, dynamic—it is effectually 'trying' to change its logical-arithmetical 'state', and, the possibility of reverting to its original, state, is low-probability but, is, one or-combinatorially-more of its possibility choices—it could revert by itself in some long-term perspective, and given that, that, possibility, is-not zero, there might-be a 'clever' way of improving it up to a useful,-probability...
(For an asymptotic-extreme-case to show probability and clever-utility may be correlated, try, two particles, and the process of re-trapping both on one side being the-same as that which released the entropy in the first place—slide the halver-partition in the same manner, at no-energy-cost, independently of the gas dynamics energies... in a few tries, the two particles are statistically-possibly re-trapped on the original side—and 'cleverness' wins somewhat...)
So, example, in the same case of gas in a dual-halves chamber, the probability of each molecule of gas being in the original-half chamber is, 1/2, 50%, 0.5, and, for multiple molecules the probability (the 'arithmetical state'), is 0.5n which for practical cases in electrochemistry on 'experimental' quantities like a micromole, by Avogadro's number, like 1018 molecules, the probability is like 0.51e18 ≈ →0, but, not-absolutely, and sigma is like 109 molecules, a billionth of the tiny sample, so by steps of a billionth it might be reverted—faster than waiting 21e18 seconds, longer than the universe is old...
(Note the smallness of 0.51e18 compared to a 'googoleth' 0.1100 ~ 0.5332, implicates that it is not-to-be-contended-with directly, but by the square-root-of-moles its process may be efficient.)
(Note also there are other variables to consider, step oscillations, 'hard' molecules taking-up some of the space, etc., but trivially herein.)
And, the possibly 'clever' design might-be a contraption, that might-exist, that makes use of the dynamical, process, of entropy, and 'recovers' some, of the entropy (maybe there's a secondary limit), by sorting and cascading the gas by half-chambers into successively denser, half-chambers, and ultimately to put it to some use—
E.g. the 'How-d'yo'-Do-dee-O-entropy-radiator'—because entropy is dynamic—periodically shuts the halver partition and measures the two halves (weight, refraction, pressure), and sorts to cascaded sorters (cf upgrading uranium to reagent grade)... and in short order by billionths-per-step extracts so-called-irrecoverable entropy energy—some...
Note the 'first obvious' secondary, limit, is that the sorting process gains positively in one-chamber-half and negatively in the other half—(aka, it half-falls-back so that it builds-out around the central density where it started)—this equates to a time-squared slower buildup, which equates to constant power, energy per time, which means, this better-suits a constant-power engine (e.g. Sterling engine), for use as a constant-power entropy-recovery recycler... but then-again note that utilizing the recovered energy will also be by adiabatic process with its lesser efficiency—(yet, at no cost)... But there may be a further-secondary-limit in the details...
Also note that technology-wise, this device recovers entropy by small-amount (micro-stage) or by small-compounded (successive-chamber-halving with greater complexity)...
Note, this is not, 'perpetual-motion' nor, 'free-generation', because, putting-it-to-use, takes its energy content—just more efficiently....
Comment: This is an 'improvement' on my 8th-grade science project 'Gibbs Free Energy'...
[under further construction] Alternatively—use a piezoelectric partition, and every time the partition is shut extract the side-vs-side energy difference of the gas-dynamical 'white noise' thermal power...
And as-always, recheck the arithmetic....
A premise discovery under the title,