5
$\begingroup$

Do you know of an elementary proof for the second law of thermodynamics, for example, from the Newton laws or perhaps some particular model in which it is equivalent/reduces to it?

My naive concept of entropy was it was some concave function of all velocities of a system, for example, $min(\{v\})$. Is it correct at all?

Improve this question
$\endgroup$
6
  • 1
    $\begingroup$ To my knowledge there is no relationship whatsoever between Newton's 2nd law of motion and the 2nd law of thermodynamics. But I'm all ears. $\endgroup$
    – Bob D
    Commented Jan 28, 2023 at 22:20
  • $\begingroup$ @BobD I used it for the instance because its simple enough. 2nd law of thermodynamics uses the entropy that i dont understand, so I tried to turn the situation and understant it using this law. $\endgroup$
    – konto
    Commented Jan 28, 2023 at 22:25
  • $\begingroup$ You can think of entropy as something similar to randomness or messiness. Just consider your room. Without your energy input cleaning it up periodically it will get more and more messy over time. $\endgroup$
    – slebetman
    Commented Jan 29, 2023 at 23:18
  • 2
    $\begingroup$ Observe that Newton's second law is unchanged by the transformation $t \mapsto -t$ (assuming $F$ does not explicitly depend on $t$). The same cannot be said of the 2nd law of thermodynamics. As such, it cannot be possible to derive the latter from the former. $\endgroup$
    – Charles Hudgins
    Commented Jan 30, 2023 at 0:33
  • 1
    $\begingroup$ Information theory is a better approach. Basically, the number of states labelled with high entropy is insanely insanely larger than the ones labeled low entropy. Then you just need operations to cause a somewhat random walk in the space and you'll end up in the high entropy states with near certain probability. There is nothing stopping you from getting into the low entropy states, but it is like dropping a cork into the ocean, picking a random spot in it, then spotting the cork right there in exactly 10 years. The cork is somewhere, but the low entropy states are almost none of the ocean $\endgroup$
    – Yakk
    Commented Jan 30, 2023 at 0:49

2 Answers 2

Reset to default
25
$\begingroup$

You cannot derive the second law of thermodynamics from Newton's laws. Boltzmann's H-theorem was intended to do that, but it's not an actual theorem: the proof is flawed. However, although it's not a theorem, it works in reality. Go figure.

Improve this answer
$\endgroup$
4
  • 1
    $\begingroup$ it works in reality. Go figure. take my angry upvote. $\endgroup$
    – AnoE
    Commented Jan 30, 2023 at 11:30
  • $\begingroup$ Boltzmann's proof is flawed, but not necessarily the theorem. See, e.g., Gibbs' H-theorem $\endgroup$
    – Roger V.
    Commented Jan 30, 2023 at 12:50
  • $\begingroup$ @AnoE Why angry? $\endgroup$
    – John Doty
    Commented Jan 30, 2023 at 17:07
  • $\begingroup$ @JohnDoty a little joke. Angry because reality dares to work, albeit the theorem / proof being wrong. ;) $\endgroup$
    – AnoE
    Commented Jan 31, 2023 at 7:53
6
$\begingroup$

Reversible Newtonian mechanics is not enough; it can describe both physical behaviour (systems in non-equilibrium state spontaneously relaxing to equilibrium state) and reversed behaviour we don't observe (systems spontaneously leaving equilibrium state and going into the non-equilibrium state).

To select the "correct" behaviour of mechanical systems consistent with 2nd law, we need additional assumption, such as assumption on the initial conditions that lead to the "correct" behaviour. Most "random" initial conditions will lead to physical behaviour. But initial conditions may be fine-tuned to lead to unphysical behaviour, where the system evolves towards states of lower entropy.

Improve this answer
$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.