A 50-Year Quest: My Personal Journey with the Second Law of Thermodynamics

I remember being thrilled by his 2015(?) piece (the really long &quot;cellular automata as universal foundation&quot; one).<p>Felt like a proper stab at combining physics + CS, thin on details, but fertile ground. Wolfram is an explorer there, barely charting the edges of an unknown continent.<p>The speed of light, light cones, and speed&#x2F;time equivalence make a ton of sense through the lens of updates propagating through a grid of cells.<p>Don&#x27;t remember the QM part so well, but from what I do remember, he proposes that probability&#x2F;alternate timelines are subject to the same computational constraints over probability space, that physical objects have in real space.<p>As an aside, entangled particles were only ever a conceptual issue, right? From an engineering perspective they seem completely practical.

I think it&#x27;s pretty obvious that the second law comes from reversibility of the microscopic laws.<p>In classical mechanics, Liouville&#x27;s theorem makes phase space density incompressible, so you get that entropy always increases. In quantum mechanics, unitarity gives the same incompressibility - the density matrix change with time is multiplying by a unitary matrix left and right, which preserves the eigenvalues, so the entropy, being sum of the log of eigenvalues, stays the same.<p>The opposite is also obvious: in a system which is irreversible, look at an ensemble of two states which evolve to a single state. The entropy before was 1 bit, after the evolution it&#x27;s 0 bits. So the system violates the second law.