Solving Statistical Physics Equations of Motion for N-Particle Systems

In summary, the conversation discusses a statistical system of N particles with a Hamiltonian, and the equations of motion for the system are derived. However, solving these equations can be time-consuming and there is a question about obtaining and solving Newton's equation of motion for the system using a functional approach. Additionally, there is a question about the concept of negative temperature.
  • #1
eljose
492
0
Let be an statistical system of N particles with their Hamiltonian..

[tex]H=\sum_{i=0}^{N}\frac{p_{i}^{2}}{2m}+V(q1,q2,...,qN) [/tex]

then you could obtain their equations of motion in the form:

[tex] dp_{i}/dt=-dH/dp_{i} [/tex] and [tex]dq_{i}/dt=p_{i}/m [/tex]

but of course if N is big you could take years and years to solve it..but there wouldn,t be an easier formula..(or an approach) to obtain and solve Newton,s equation of motion for this system (considering stochastic or similar) by means of a functional of the q,s in the sense [tex]Q(q1,q2,q3,q4,...qN) [/tex]
 
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  • #2
Was there a question in there?
 
  • #3
may i know what is the meaning of negative temperature?
 

Related to Solving Statistical Physics Equations of Motion for N-Particle Systems

1. What is statistical physics and why is it important?

Statistical physics is a branch of physics that deals with the study of physical systems on a statistical level, rather than a microscopic or macroscopic level. It involves using statistical methods to understand the behavior of large systems composed of many particles, such as gases, liquids, and solids. This is important because it allows us to make predictions about the behavior of these systems, which can have practical applications in fields such as engineering, materials science, and thermodynamics.

2. What are equations of motion in statistical physics?

Equations of motion in statistical physics refer to mathematical equations that describe the time evolution of a physical system. These equations take into account the interactions between particles, as well as external forces and constraints, and allow us to predict the future state of the system based on its current state.

3. How do you solve equations of motion for N-particle systems?

Solving equations of motion for N-particle systems involves using mathematical and computational methods to solve the equations and obtain a solution that describes the behavior of the system. This can be a complex and time-consuming process, as it requires taking into account the interactions between all N particles in the system.

4. What are some common techniques used to solve statistical physics equations of motion?

There are several common techniques used to solve equations of motion in statistical physics, including Monte Carlo simulations, molecular dynamics simulations, and mean-field approximations. These techniques involve using numerical methods to solve the equations and obtain results that can be compared to experimental data or used to make predictions about the system.

5. What are some applications of solving statistical physics equations of motion?

The ability to solve statistical physics equations of motion has many practical applications. For example, it can be used to understand and predict the behavior of materials under different conditions, such as temperature and pressure, which is important in fields like materials science and engineering. It can also be used to study and model complex systems, such as biological systems, and to improve our understanding of fundamental physical phenomena, such as phase transitions and critical phenomena.

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