# Questions tagged [poincare-recurrence]

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25 questions
1answer
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### Relation between correlation functions and Poincaré recurrence time

When deducing Markovian quantum master equation, supposing the total Hamiltonian is the following form: $H=H_{S}+H_{B}+H_{I}$ where $H_{S}$ is the Hamiltonian for the quantum system, $H_{B}$ is ...
1answer
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### Poincaré recurrence theorem with irrational frequencies?

The Poincaré recurrence theorem states that, for a bound phase space, the system will return to a state very close to the initial conditions, in some finite time $\tau$. For example, let's say I have ...
0answers
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### Resolvoing the apparent contradiction between the Poincare recurrence theorem and second law of thermodynamics

I am personally a bit troubled by the apparent contradiction between second law of thermodynamics and the Poincaré's recurrence theorem. I have seen lots of arguments which seem to resolve the issue ...
1answer
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### When intersections of trajectories in Poincare sections are possible?

If we get intersections of some "trajectories" in non-standard 2D Poincare sections, that have been obtained from numerical integration of Hamilton equations for autonomous system in 2D coordinate ...
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### Dimension of Poincaré Map

I am used to seeing bi-dimensional Poincaré maps, as the ones shown in this post: Poincaré maps and interpretation In that example, one manages to draw a bi-dimensional map because the number ...
3answers
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### Why did Poincaré's recurrence theorem represent Harm to Kinetic Theory of Gases?

Poincaré's recurrence theorem remained as far as I know, unproven until 1919 when Caratheodóry proved it. Why then did it represent an issue to Boltzmann? Boltzmann died in 1906, did he not know about ...
1answer
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### Example of Poincare recurrence theorem?

Is it possible to explain Milankovitch cycles (or some other arbitrary planetary configuration that recurs to some approximation) in terms of the Poincare recurrence theorem? More generally, is ...
1answer
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### Classical mapping of kicked harper model

The Hamiltonian of kicked harper model is given by $$H=K\cos(p)+[K\cos(x)\sum_{n=-\infty}^{+\infty}\delta(t-n)]$$ where $\delta$ function term represents the effect of very narrow pulses of an ...
2answers
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### Calculating Poincare recurrence times

I am interested in calculating the Poincare recurrence time of a physical system (i.e. a system with with continuous time evolution). I have seen physics papers giving estimations of the recurrence ...
1answer
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### Is the Poincaré theorem valid for our universe? [duplicate]

Poincaré tell us (roughly speaking) that any hamiltonian system come up arbitrarily close to the initial condition if you wait enough time. For example, this theorem is valid for gases, and in ...
2answers
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### Must the universe recur, be infinite, or be infinitely divisible?

When I was an undergraduate, I had this thought: Suppose that everything is made of atoms (I mean, pieces which cannot be separated further) and the universe has a finite amount of space. Let $N$ be ...
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### Poincaré recurrence theorem in scattering state

According to https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem#Quantum_mechanical_version the most recent paper is Schulman, L. S. (1978). "Note on the quantum recurrence theorem". Phys....
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### Poincare recurrence time of the Universe

I've read around a bit, and it seems to be universal that the notion of a Poincare recurrence time for the universe exists. And it seems to be debated that the universe can be given an entropy, as it ...
3answers
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### Poincaré Recurrence and Immortality [closed]

If, as Luboš Motl says, Poincaré recurrence is relevant for our universe, does this mean (1) that, after I die, I'll one day live through my life again after the same physical pattern that is ...
0answers
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### The fate of Poincaré recurrence with the Big Rip

Recently, there has been a lot of talk in the media about the "Big Rip". It most certainly resulted from the paper by Marcelo M. Disconzi and Thomas W. Kephart where they have figured out a ...
1answer
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### Does Poincare recurrence imply that a photon shot into a box will exit the way it came in?

If you have a big closed cube that has perfectly mirrored surfaces on the smooth flat walls or faces of the cube and only one corner has a tiny 'entrance', a narrow hole at a specific angle, say '...
2answers
637 views

### Is entropy related to Poincare recurrence time?

One of the ideas involved in the concept of entropy is that nature tends from order to disorder in isolated systems. But we even know that Poincare recurrence time also is a particular time after ...
1answer
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### Poincaré maps and interpretation

What are Poincaré maps and how to understand them? Wikipedia says: In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the ...
3answers
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### Is Poincare recurrence relevant to our universe?

If the theory of everything indicates a singularity-free and finite universe, will Poincare recurrence be relevant to the universe? If so, is there any interesting physical consequence, e.g. in ...
1answer
242 views

### What is the probability of ice in boiling water?

Ice crystals are spatially ordered, and in every randomness there is a low possibility of temporarily order. If given enough boiling water, and sufficient time, could local clusters water molecules ...
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### Poincare recurrence and the multiverse

In this paper Susskind claims that a stable de Sitter universe is problematic (among other things) due to the existence of Poincare recurrence, which happen because of finite entropy. I disagree that ...
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### Is large-scale “time reversal” (Poincaré recurrence) possible given infinite time?

The following are some assumptions I'm basing my question on, from what (little) I understand of physics. I list them so an expert can (kindly) tell me where I'm going wrong. There is a probability ...
4answers
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### Why aren't we Boltzmann brains in an infinite universe?

Either space is finite or it is infinite. a) - If space is infinite in extent, either it is thermal over an infinite volume, or it is in the vacuum state for most of it. If it is thermal, infinity ...
3answers
1k views

### Is decoherence even possible in anti de Sitter space?

Is decoherence even possible in anti de Sitter space? The spatial conformal boundary acts as a repulsive wall, thus turning anti de Sitter space into an eternally closed quantum system. Superpositions ...
1answer
961 views

### Does the heat death of the universe really imply a maximum entropy state *all* of the time? Or most of the time?

Statistically speaking, you're going to still encounter deviations from equilibrium, even though the expected value is equilibrium. But these rare deviations from equilibrium - which are inevitable - ...