# Questions tagged [phase-space]

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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### Weak Equality & Strong Equality?

I have been trying to understand the meaning of these concepts: Weak $(\approx)$ and Strong $(=)$ Equality in the Dirac-Bergmann Algorithm for Hamiltonian Constrained Systems. I have already read ...
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### Canonical ensemble, ergodicity and Liouville’s equation

I understand that in Statistical Mechanics Liouville’s equation applies to the probability density of ensembles where microstates’ trajectories are governed by Hamiltonian dynamics. However I’m ...
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### Is it possible to use topology arguments to find analogies in thermodynamic systems?

I was contemplating whether, given the mathematical structure of thermodynamics, it might be possible to restate some of its most important propositions—or even all of them—purely in topological terms....
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### Group actions confusion

I have been using results from this paper in calculations. In sections 2.4 and 3.4 they perform a canonical transformation into new coordinates consisting of constants of motion. They then construct ...
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### Can we reduce the entropy of a system arbitrarily by sending out a photon after arbitrary delay?

I am not asking whether this is practically feasible given current technology. Rather I'm asking whether it is possible in principle given current laws of physics. Suppose we have a system with a ...
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### Are the canonical momentum and the corresponding generalized coordinates independent? [duplicate]

I know that for a lagranian $L=L(q_i, \dot{q_i},t)$ the canonical momentum is given by $p_i = \frac{\partial L}{\partial \dot{q_i}}$. The lagrangian being a function of the generalized coordinate, I ...
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### Is it possible to understand in simple terms what a Symplectic Structure is?

I would like to understand what a Symplectic Structure is, and its implications in Classical Mechanics (Phase Space), but in pre-grade terms (If that could be possible). I have not taken any ...
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### Lorentz-invariant phase space integral

Consider the following Lorentz invariant integral associated to a $2\to 2$ scattering: \begin{equation*} I = \int \frac{d^3\mathbf{p_3}}{(2\pi)^3 2E_3} \int \frac{d^3\mathbf{p_4}}{(2\pi)^3 2E_4} \...
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### Problems with Kerson Huang's derivation of NVE ensemble entropy

So I'm currently studying statistical mechanics from different textbooks, but my professor suggested Kerson-Huang for a general derivation of entropy in microcanonical ensembles. In chapter 6.2 is ...
1 vote
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### Why $q,p,Q,P$ are Independent Variables when Using Generating Functions?

In Hamiltonian formalism, specifically generating functions, why do the variables $q, p, Q, P$ are treated as independent when finding the equations that arise from the generating function? I ...
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### Why do we need a Poisson bracket structure?

Let me start by asking why we need a Poisson bracket like structure on the Hamiltonian phase space? Say we have a constraint, why do we go through the trouble of defining a Dirac bracket structure on ...
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### Regarding Poisson and Dirac brackets [duplicate]

The question starts with why Poisson brackets (in constrained systems) gives different relation if we substitute the constraints before or after expanding the bracket, and why this difference in ...
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### Regarding Poission structure of Hamiltonian phase space

Why exactly do we need $$\{q^i,p_j\}=\delta^i_j,$$ where $\delta^i_j$ is Kronecker delta and $\{\cdot,\cdot\}$ is the Poisson bracket? What happens to the phase space structure if these fundamental ...
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### Decoherence model of two qubits interacting with correlated multimode fields - open quantum system

I read paper on open quantum system, that talk about non-Markovian process and memory effects. they described the system as a generic decoherence model of two qubits interacting with correlated ...
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### Constrained Hamiltonian problems [closed]

What happens to the poisson bracket structure of Hamiltonian phase space if We have some constraints in $p$ and $q$. What physical aspects this structure represents?
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### An example of symplectomorphism that is not a canonical transformation

I want to check my understanding on the difference between symplectomorphism and canonical transformation. This is a follow-up of my previous post. (A) A map $(q,p)$ to $(Q,P)$ is called a ...
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### Partition function with Hamiltonian depending on parameter

Given a Hamiltonain $H(p,q)$, I know that the classical partition function for a single particle is given by an integral over the phase space $$Z_1 = \frac{1}{h^3} \int e^{-\beta H(p,q)} d^3pd^3q$$ ...
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### How can we design the global structure of the phase space?

I want to know how to design a classical mechanical system that has a phase space $M$ with a nontrivial global topology. If I naively consider a system in which the generalized coordinate \$q_1,\cdots,...
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