Several years before it became fashionable to dismiss everything as a Makov chain.
Given a simple history can be mapped into a higher dimensional state, Markov chains are much more common than they first seem, so it's basically* always possible to dismiss any physically implementable system as "a Markov chain" if you're so inclined.
* While I wouldn't be surprised if someone has come up with laws of physics that can't be described by a Markov chain, mere quantum mechanics can.
Quantum mechanics can be described as a Markov chain? That seems plausible but I haven't worked with MCs enough to see exactly how. Could you please elaborate? It seems interesting.
If you want to study a quantum mechanical system in equilibrium at inverse temperature β, the interesting quantity is the partition function Z = tr exp[-β H]. This can be converted into a path integral Z = ∫ dφ exp[-S[φ]] which can be importance-sampled via the Metropolis-Hastings algorithm [mh] via Markov-chain Monte Carlo.
This approach is commonly used in lattice field theory [lft], where the Hamiltonian H is that of a discretized spacetime (or the problem is formulated in terms of the action S to begin with).
Real-time problems in quantum mechanics involve exp[i t H] which brings a horrible complication called the sign problem [sign]. The one-sentence summary is that exp[-β H] is positive-definite but exp[i t H] is not and it's not clear how to incorporate a complex Boltzmann weight as a probability for MCMC.
A Markov process is a random process where the new state only depends on the old state, not anything else. This can be stretched to include almost anything, since you can expand the definition of the state to record history or whatever you want, although you may make the process much more difficult to work with mathematically. In other words, the fact that something may be a Markov process is generally not interesting, because it is a very broad definition, and doesn't guarantee any interesting properties without further assumptions.
The wavefunction in QM doesn't evolve randomly, so I would say it is not technically a Markov process. On the other hand you can create a theory of observables derived from QM that is "random" (depending on your interpretation of quantum mechanics).
You will have a hard time constructing Markov Chain that correctly models the real-time evolution of physical quantum-mechanical observables. The problem is that the transition matrix that governs quantum-mechanical evolution is exp[i t H], which is not a well-formed probability distribution.
I would have said something very close to zeofig's answer, with the one significant change being to say that a deterministic system is itself a very boring kind of Markov chain where all states' transition probabilities are exactly 0 or 1.
Still a misnomer in my opinion, but I noticed that this part of the algorithm was missing from all the articles that followed (mine included). People are basically implementing sudoku solvers :)
Since people started using marketing tactics to promote themselves. WFC is a $100 name for a $1 concept. Other entries in the tech hall of shame are mersenne twister and dependency injection
>There are two main complaints from academic community concerning this work, the first one is about "reinventing and ignoring previous ideas", the second one is about "improper naming and popularizing", as shown in some debates in 2008 and 2015.[33] In particular, it was pointed out in a letter[34] to the editor of IEEE Transactions on Neural Networks that the idea of using a hidden layer connected to the inputs by random untrained weights was already suggested in the original papers on RBF networks in the late 1980s; Guang-Bin Huang replied by pointing out subtle differences.[35] In a 2015 paper,[1] Huang responded to complaints about his invention of the name ELM for already-existing methods, complaining of "very negative and unhelpful comments on ELM in neither academic nor professional manner due to various reasons and intentions" and an "irresponsible anonymous attack which intends to destroy harmony research environment", arguing that his work "provides a unifying learning platform" for various types of neural nets,[1] including hierarchical structured ELM.[28] In 2015, Huang also gave a formal rebuttal to what he considered as "malign and attack."[36] Recent research replaces the random weights with constrained random weights.[6][37]
But at least it's easier to say, rolls off the tongue smoothly, and makes better click bait for awesome blog postings!
I also love how the cool buzzwords "Reservoir Computing" and "Liquid State Machines" sounds like such deep stuff.
Yukio-Pegio Gunji, Yuta Nishiyama. Department of Earth and Planetary Sciences, Kobe University, Kobe 657-8501, Japan.
Andrew Adamatzky. Unconventional Computing Centre. University of the West of England, Bristol, United Kingdom.
Abstract
Soldier crabs Mictyris guinotae exhibit pronounced swarming behavior. Swarms of the crabs are tolerant of perturbations. In computer models and laboratory experiments we demonstrate that swarms of soldier crabs can implement logical gates when placed in a geometrically constrained environment.
The difference between Deepak Chopra's abuse of Quantum Physics terminology and WFC's is that WFC actually works and is useful for something, and its coiner publishes his results for free as open source software and papers, so he deserves more poetic license than a pretentious new-age shill hawking books and promises of immortality for cash like Deepak.
Here are some notes I wrote and links I found when researching WFC (which is admittedly a catchier name than "Variable State Independent Decaying Sum (VSIDS) branching heuristics in conflict-driven clause-learning (CDCL) Boolean satisfiability (SAT) solvers"):
Here are some notes I wrote and links I found when researching Wave
Function Collapse (WFC). -Don Hopkins
Wave Function Collapse
Maxim Gumin
Paul Merrell
https://paulmerrell.org/research/
https://paulmerrell.org/model-synthesis/
Liang et al
Jia Hui Liang, Vijay Ganesh, Ed Zulkoski, Atulan Zaman, and
Krzysztof Czarnecki. 2015. Understanding VSIDS branching heuristics
in conflict-driven clauselearning SAT solvers. In Haifa Verification
Conference. Springer, 225–241.
WaveFunctionCollapse is constraint solving in the wild
https://escholarship.org/content/qt1f29235t/qt1f29235t.pdf?t=qwp94i
Constraint Satisfaction Problem (CSP)
Machine Learning (ML)
It splits an image to cells by using convolutions, derives a set of constraints of how cells can be combined and then generates combinations that satisfy the constraints. It's a form of machine learning based on combinatorial optimisation, really.
Far as I can tell it doesn't apply any Markov assumptions anywhere, but I might just not have noticed it so please prove me wrong on that one.
Given a simple history can be mapped into a higher dimensional state, Markov chains are much more common than they first seem, so it's basically* always possible to dismiss any physically implementable system as "a Markov chain" if you're so inclined.
* While I wouldn't be surprised if someone has come up with laws of physics that can't be described by a Markov chain, mere quantum mechanics can.