# Tagged Questions

A notional even-dimensional space representing all relevant states of a dynamical system; it normally consists of all components of position and momentum/velocity involved in that unique specification. Use for both classical and quantum physics.

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### Extending the ergodic theorem to non-equilibrium systems

I try to make this as short and concise as possible. For equilibrium systems in statistical mechanics, we have the Liouville's theorem which says that the volume in phase space is conserved when the ...
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### Volume as a choice of measure in phase space

For equilibrium systems, we expect the Liouville theorem to hold. This theorem states that the density function of the states of the system is a constant of motion, which in turn can be translated ...
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### What is the correct relativistic distribution function?

General Statement and Questions I am trying to figure out the proper way to model a velocity/momentum distribution function that is correct in the relativistic limit. I would like to determine/know ...
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### Phase space orbit for a projectile [closed]

After playing around with drawing the phase space orbit for a harmonic oscillator I started wondering about the case for a free falling object. So the equations of motion are: $$P = P_0 + mgt$$ ...
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### Area of phase space of Harmonic oscillator

We all know that the phase trajectory of an undamped linear harmonic oscillator is an ellipse. But when we calculate the area of the ellipse we find it does not depend of mass of the particle. Why is ...
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### Preservation of phase space volume: the extension from “small” times to generic times

Having a classical system whose evolution is described by $$\dot{\phi_t}(x) = f(\phi_t (x))\\ \phi_0 (x) = x$$ denoting with $\phi_t (x)$ the evolution for a time t of the ...
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### Density of states of classical harmonic oscillator in phase space

Since all classical harmonic oscillators are ellipses in phase (position-momentum) space, and since the entire phase trajectory of a given system (with a fixed rigidity and mass factor) can be ...
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### Calculating the number of particles in phase space

I'm looking at the first part of question 7 here (I'm a mathematician trying to self teach some physics, this isn't a homework assignment so I'm just in need of hints)! I'm struggling to make sense of ...
During my undergrad physics classes, I've come across several seemingly related phenomena dealing with $h$ and phase space in quantum mechanics. Let $T_x$ be a translation operator by $x$ in ...
The phase space version of Feynman's path integral expression for the free particle propagator involves a (formal) sum over paths in phase space with fixed $q$ endpoints and (as far as I'm aware) ...