Can the universe be described by a Markov chain? This may be a fairly basic question as I don't have a strong background in physics.  I intuitively thought that the universe must be able to be described by a Markov chain. That is, I thought you could feed the current state of the universe into a process and it would spit out the next state conditional on the laws of the universe.  However, I have found no mention of the universe as a Markov chain outside of speculations on message boards.
Can the universe be described as a Markov chain or is there some reason to suggest that the next state in the universe is dependent on more than just the current state and constant universal laws?
 A: The problem is that Markov chains are inherently lossy--- so in physics as it is commonly understood today, the answer is no. A Markov chain will always lose information about the initial state, as it relaxes to a stable distribution, while a quantum mechanical system does not do this. The modern understanding of a physical system is as a quantum markov chain, which is the same as a classical Markov chain with probability amplitudes taking the place of probabilities.
But I believe it is an open question if you can approximate quantum dynamics by a Markov dynamics, so that it resembles the real thing. This is related to this question and answer: Stochastic processes and wavefunction collapse
A: I wanted to clear up a few misconceptions in the responses. 
First, a markov chain system must be independent of its past.  However, if the state space of the possible states is expanded to include the residual history, then a system which "remembers its past" becomes a markov chain if the state space itself is large enough to include all the states with the recorded past history.
Non linear phenomena are definitely markov chains, and the universe appears to be a markov chain provided you define the state space as the exact microstate.
Markov chains are not necessarily time continuous or time discrete.
A: Systems where the past history is not important can be described by Markov chains. 
However when the system remembers the past we cannot use Markov chains for instance
in non-linear phenomena.
A: For more thoughts on the universe being a Markov chain, please google "Markov Chain Universe".  It is a truly fantastic web site dedicated to this topic.  Who do you think made it? ;)
Whether or not you choose to accept the axioms of the theory, it is a mind bending experience to think about.
It is a lot like first understanding that the earth is a sphere, rather than a flat plane.
Except in this case, it is understanding that the Markov chain probability of the universe exists as an orthogonal metric to the measure understood by thermodynamic entropy.
Thus, there exists a completely new probability, which appears to correspond to our macroscopic concept of complexity.
Please stop by and take a gander and ask lots of questions. 
