# Markov property: compatible with momentum?

• I
• lolcopters
In summary, the conversation discusses whether a system of two interacting atoms can have the Markov property, which means that the future positions of the atoms depend only on their current position and not the past. The speaker is unsure due to the atoms' momentums, which are a property of the present state but depend on past states. The other person clarifies that the Markov property is dependent on the variables chosen to define the state, and these may differ depending on whether actual atoms or point particles are considered. The conversation also raises the question of whether other variables like mass, velocity, and acceleration should be included in the definition of state.

#### lolcopters

Say I'm simulating the movements of two interacting atoms. Could this system have the markov property (the future positions of the atoms depend only on the current position, not the past)?
What's got me on the fence are the atoms' momentums: it's a property of the present state (at time t, the momentum is p), but its value depends on past states. So does anyone know if a system like this could have the markov property?
Thanks

You misunderstood what Markov is about. Of course, the state of any system at time t0 depends on what happened at times t < t0. But in a Markovian process, there is no memory of how the state at time t0 was reached. All that is important is that the state at time t0 completely describes the system (and its future evolution).

In the case of two atoms governed by a known Hamiltonian, given the wave function ψ(t0) of the two-atom system, one can calculate ψ(t) for any t > t0. No need to know the wave function for any time < t0.

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lolcopters
lolcopters said:
Say I'm simulating the movements of two interacting atoms. Could this system have the markov property (the future positions of the atoms depend only on the current position, not the past)?

It isn't meaningful to ask whether a physical system has the markov property until you say what variables you will choose to define a "state". A physical system may have the markov property when one definition of "state" is used and not have it when a different definition is used.

Are you considering actual atoms - or just thinking about "point particles" ?

You only mention "position" as the variables involved in your definition "state" ? Did you intend to omit variables like mass, velocity and acceleration ?

DrewD