Posts by Marc Serra

I've just taken a look at this Quora question and I'm surprised too at the (unusually) poor quality of the answers. I can think of two approaches to see that a system does not violate the second law of thermodynamics.

The first one is very general: You assume something about the system (Such as that the dynamics of the system [both atoms and pawl] is time-reversible) and derive a fluctuation relation, which tells you that the probability of an entropy-increasing event is always larger or equal to the probability of an entropy-decreasing event. Then you can look at every ingredient in your system to check that it satisfies the assumptions of the fluctuation theorem (For example, motion of a mass-spring system such as the pawl is time-reversible because if you watch the motion in reverse you get an equally physically valid trajectory, which is true for Hamiltonian systems in general).

https://en.wikipedia.org/wiki/Crooks_fluctuation_theorem
https://en.wikipedia.org/wiki/Microscopic_reversibility

This is a very abstract procedure but it guarantees that if your system does not contain 'naughty' elements (That don't follow Hamiltonian dynamics or break time reversal symmetry somehow), then it is not going to violate the second law. There are no such elements in the racthet-and-pawl device as it is typically drawn, with or without gas on the other side.

The second one (that is probably what you are looking for) is to simulate the system (either using a computer or mentally) and seeing what can go wrong. Looking at this drawing of a racthet and pawl system:

http://i.kinja-img.com/gawker-…/t83tjdx6klcwghgqeosb.png

Let's try a bit of mental simulation: What happens after the pawl jumps from one tooth to the next one. Option (a): The elastic potential energy in the pawl gets dissipated somehow. If that's the case, then we're done. Your system is not Hamiltonian (has energy loss) but it's dissipating energy somewhere (heating a cold reservoir) in addition of producing work. If the cold reservoir is too hot, there will be energy transfer from the reservoir to the pawl (i.e. allowing it to jump up sometimes and letting the ratchet go in reverse). If you include the dynamics of the reservoir that takes the potential energy from the pawl, then the whole system will be microscopically time-reversible and will follow the fluctuation theorems. What if there is no reservoir where the pawl's potential energy can go? Well, then after the first jump it will keep oscillating with an amplitude equal to the height of the teeth. This will allow the ratchet to move in any direction, and the whole system will not work.

The explanation that I've provided here is very simplistic. There are papers on the topic that are many pages long and provide a rigorous and detailed treatment, but this should give you a rough idea. If you are computationally inclined, it is not *too* hard to simulate a system like this one.

Quote from Contrarian

BTW, your paper sure goes out of its way to lead to that conclusion when you keep mentioning Brownian motion and Feynman's ratchet and pawl. Maybe you should have been more clear what you are trying to do.

Neither the Feynman ratchet nor Brownian motion contradicts the second law in any way, and this has been known for more than 60 years. The audience of the paper is expected to know that. Scientific papers are limited in length and thus cannot explain all prior knowledge required to understand them.

Quote from Lou Pagnucco

An Arxiv-preprint which, if correct, appears to challenge the 2nd Law ---

A mechanical autonomous stochastic heat engine

ABSTRACT: Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using e.g., thermal cycles implemented in optical traps. However, the recent demonstrations of stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle, and consume more energy than they produce. This Report presents a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.

http://arxiv.org/abs/1601.07547

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Quote from H-G Branzell

I will believe it the day that I can buy a fridge without electric cord. A self heating / cooling house would also be very nice, thanks.

I'm a co-author on that pre-print. Our system does not violate or challenge the second law of thermodynamics in any way (and this should be obvious to anyone who has actually read the paper). The negative thermal conductivity phenomenon requires two low temperatures (Tc and Th, Th > Tc) and a hot one (Tw). Energy flows from Th to both Tc and Tw in such a way that the increase in entropy at Tw and Tc together is greater than the decrease in entropy of Th. Therefore, it satisfies dS_tot > 0.

You can think of it as operating a termoelectric between a temperature of 0 ºC and 100ºC, and using the resulting power to heat a resistor to 200 ºC. In such a system, energy is flowing from the 100ºC reservoir to the 200ºC resistor. Our point is that a simple nonlinear system (essentially a resonating guitar string) can present this phenomenon.