# How is the 2nd law of thermodynamics related to the uncertainty principle?

• quantumkiko
In summary, the article discusses how the Second Law of Thermodynamics can be derived from classical systems, and shows that the behavior of matter has a QM origin.
quantumkiko
Does this suggest that the 2nd law of thermodynamics has a quantum mechanical origin?

No, since thermodynamics can be derived from statistics of ideal classical bodies (and quantum evolution is time symmetric).

People have indeed shown such a relation. I noticed a professor here has posted a popularized article about this on his door (I think it may be scientific american, so I may be able to provide a link). I'll check next time I pass by his door.

cesiumfrog said:
No, since thermodynamics can be derived from statistics of ideal classical bodies (and quantum evolution is time symmetric).
Yes, quantum evolution is time symmetric. But that doesn't prevent entropy from increasing in one direction. Hence the notion of "thermodynamic arrow of time" (time increases in the direction of entropy increase).

Also, statistical mechanics is usually taught as a quantum theory (working with the multiplicity of states having the same macroscopic state values of, for instance, the total energy). So this doesn't need to be an issue of "ideal classical bodies".

Usually ideas relating entropy increase and quantum mechanics use the fact that as things interact their states become entangled.

quantumkiko said:
How is the 2nd law of thermodynamics related to the uncertainty principle?... Does this suggest that the 2nd law of thermodynamics has a quantum mechanical origin?

What does "this" mean?! You haven't described any statement/fact/experiment/theory to refer to!

The Second Law is derivable from classical systems, so no, I wouldn't say it has a quantum mechanical origin.

Mapes said:
The Second Law is derivable from classical systems, so no, I wouldn't say it has a quantum mechanical origin.
Did you read the other posts?

Anyway, I checked the professor's door and it is still up. I can't find a free link to it, but googling I did find someone who put up an editorial of the article and goes over the main points:
http://wwwrsphysse.anu.edu.au/~tas110/Teaching/Lectures/L5/Material/Lloyd06.pdf
You can get the reference to the main article from there.

Thanks for the link. OK, I see what you mean; the behavior on which the Second Law relies has a QM origin (because the behavior of all matter has a QM origin). My point was only that one can derive the Second Law from classical ensembles (as Gibbs did) and apply it to all sufficiently large systems with knowing any QM. But you're right; a deeper knowledge of randomness is valuable and will no doubt advance our science.

## 1. How is the second law of thermodynamics related to the uncertainty principle?

The second law of thermodynamics states that the total entropy of a closed system always increases over time. This is related to the uncertainty principle, which states that it is impossible to know the exact position and momentum of a particle simultaneously. This means that there is a fundamental limit to our ability to predict the behavior of a system, and this uncertainty contributes to the increase in entropy.

## 2. Can you explain the connection between the second law of thermodynamics and the uncertainty principle in simpler terms?

The second law of thermodynamics can be thought of as a statement about the direction of time - things tend to become more disordered over time. The uncertainty principle adds to this by saying that even if we knew all the information about a system at a given time, we cannot accurately predict its future behavior due to the inherent uncertainty in the position and momentum of its particles.

## 3. Is there a mathematical relationship between the second law of thermodynamics and the uncertainty principle?

Yes, there are mathematical relationships between the two principles. For example, the entropy of a system can be calculated using statistical mechanics, which is based on the principles of quantum mechanics that underlie the uncertainty principle.

## 4. How does the second law of thermodynamics apply to real-world systems?

The second law of thermodynamics applies to all physical systems, including those in the real world. It is a fundamental law of nature that governs the behavior of energy and matter, and it has been extensively studied and observed in various systems, from the microscopic level of atoms to the macroscopic level of the universe.

## 5. What are the implications of the relationship between the second law of thermodynamics and the uncertainty principle?

The connection between these two principles has significant implications for our understanding of the behavior of physical systems. It highlights the inherent limitations in our ability to predict the future and emphasizes the importance of considering the probabilistic nature of quantum mechanics in our understanding of thermodynamics.

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