Solving the Langevin Equation w/ Newton's Second Law

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In summary, the conversation discusses reconciling the Langevin equation with Newton's Second Law and how they appear to be different. The equation includes ma on one side and a sum of forces on the other, which is consistent with the 2nd law. The concern may be the H(t) term, but upon further consideration, the question may not have a valid point.
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ehrenfest
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[SOLVED] langevin equation

Homework Statement


http://en.wikipedia.org/wiki/Langevin_equation
Can someone explain to me how to reconcile the Langevin equation with Newton's Second Law? They are clearly different and I cannot think of a satisfactory reason why!


Homework Equations





The Attempt at a Solution

 
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  • #2
why are they clearly different? i don't seem to get you. it looks like there's ma on one side, and a sum of forces on the other side. looks perfectly like the 2nd law to me. is it the H(t) term you're worrying about?
 
  • #3
Now that I think about, I don't see the point of my question either.
 

What is the Langevin equation?

The Langevin equation is a stochastic differential equation that describes the motion of a particle under the influence of random forces. It is commonly used in statistical mechanics to model the dynamics of Brownian motion.

What is Newton's Second Law?

Newton's Second Law of Motion states that the force acting on an object is equal to the mass of the object times its acceleration. In other words, the net force on an object determines its acceleration.

How does Newton's Second Law relate to the Langevin equation?

The Langevin equation incorporates Newton's Second Law into its formulation by including a term for the random force acting on the particle. This allows for a more accurate description of the particle's motion in a stochastic environment.

What is the significance of solving the Langevin equation?

Solving the Langevin equation allows scientists to make predictions about the behavior of particles in stochastic systems. It is a fundamental tool in understanding and analyzing complex systems, such as those found in statistical mechanics and molecular dynamics.

What are some challenges in solving the Langevin equation with Newton's Second Law?

One of the main challenges in solving the Langevin equation is accurately modeling the random forces acting on the particle. This requires a deep understanding of the system and can be computationally intensive. Additionally, the equation may have multiple solutions, making it difficult to determine the most accurate one.

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