How does the Lagrangian apply to Brownian motion?

In summary, the Lagrangian is a mathematical tool used to describe the motion of particles in a system, including Brownian motion. It takes into account the energy and forces acting on the particles to determine their trajectory. By using the Lagrangian, scientists can better understand the complex and random movement of particles in Brownian motion, which has implications in various fields such as physics, chemistry, and biology.
  • #1
Steve Zissou
49
0
Hello, how do we apply the idea of the Lagrangian to a Brownian motion? I guess what I mean is what is the Lagrangian functional form for a Brownian motion?
Thanks
 
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  • #2
Perhaps that's the wrong question. How about this: can anyone point me toward a book in which the Lagrangian for Brownian motion is explained, such that an idiot can understand it?
Thanks
 
  • #3
Steve Zissou said:
Perhaps that's the wrong question. How about this: can anyone point me toward a book in which the Lagrangian for Brownian motion is explained, such that an idiot can understand it?
Thanks

Isn't google your friend ? :smile:

http://www.google.com/search?q=Lagr...s=org.mozilla:en-US:official&client=firefox-a

I am not sure about any book in which this topic has been explained.
 
  • #5
sankalpmittal said:
Isn't google your friend ? :smile:

http://www.google.com/search?q=Lagr...s=org.mozilla:en-US:official&client=firefox-a

I am not sure about any book in which this topic has been explained.

Look I'm sure you are a nice guy and all, but I'm not really looking for a "Hey man, try google" answer. What do you think? Do you think I've googled the topic before posting here?
I'm looking for help, not sarcasm.
 
  • #7
Not sure if this is exactly what your looking for - but an interesting foundational stat mech discussion re "crucial distinction between two kingdoms of Hamiltonian/Lagrangian mechanics" with lessons drawn from Brownian motion: http://arxiv.org/abs/1101.0571
 
  • #8
malreux said:
Not sure if this is exactly what your looking for - but an interesting foundational stat mech discussion re "crucial distinction between two kingdoms of Hamiltonian/Lagrangian mechanics" with lessons drawn from Brownian motion: http://arxiv.org/abs/1101.0571

Thanks!
 

1. What is the Lagrangian of Brownian Motion?

The Lagrangian of Brownian Motion is a mathematical expression that describes the dynamics of a particle moving in a random environment. It takes into account the random forces acting on the particle, as well as its position and velocity. It is used to model the behavior of particles in various fields, such as physics, chemistry, and biology.

2. How is the Lagrangian of Brownian Motion derived?

The derivation of the Lagrangian of Brownian Motion involves applying the principles of statistical mechanics to a system of particles interacting with a random environment. This involves considering the random forces acting on the particles and using statistical methods to determine their effects on the particle's motion.

3. What is the significance of the Lagrangian of Brownian Motion?

The Lagrangian of Brownian Motion is significant because it allows us to mathematically model and understand the behavior of particles in random environments. It has applications in many fields, including physics, chemistry, and biology, and has helped scientists gain insights into complex systems.

4. How does the Lagrangian of Brownian Motion relate to other mathematical models?

The Lagrangian of Brownian Motion is closely related to other mathematical models, such as the Langevin equation and the Fokker-Planck equation. These models also describe the motion of particles in random environments, but the Lagrangian approach allows for a more comprehensive understanding of the system's dynamics.

5. Can the Lagrangian of Brownian Motion be applied to real-world systems?

Yes, the Lagrangian of Brownian Motion can be applied to real-world systems. It has been used to study the motion of particles in various environments, such as fluids, gels, and biological systems. It has also been applied in fields such as finance and economics to model the behavior of markets and stock prices.

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