Can concentration gradients be related to information?

[Mike S.]

TL;DR Summary

A cell contains K+ ions on the inside and Na+ ions on the outside of an impermeable membrane. Can you relate the potential energy of the chemical potential (for example the Nernst potential) to information about the ions (Landauer principle)?

I was reading a great thread that pointed me to Robert Alicki, “Information is not physical“ (https://arxiv.org/abs/1402.2414). My that appeals to me, based on the apparent fruitlessness of understanding the system otherwise. But I don't know if it's even published, and even if "everybody has been lying to you" is the most common explanation for why you get confused about physics, it's not the only one. Oh, and I should note the recent peer-reviewed alternative position that information is equivalent to mass and energy.

I'll simplify a cell a little here, turning it into a membrane between two halves of a chamber. On one side, we have 1 molar NaCl in water (we'll say it's a halophile...) and on the other we have 1 M KCl (I'll only use this here to keep the osmotic effects under control). There are protein channels in the membrane that can be opened or shut, which allow either Na+ or K+ to pass through.

The energy that can be extracted can be expressed in a rather long-winded fashion in the Nernst potential - RT/zF ln Q, where Q is the reaction quotient, here the concentration of the ion (the one we would open the channel for, let's say Na+) on the inside and outside of the cell. It represents the voltage (a store of the energy which can be measured over the cell membrane if the channel is opened). The Faraday constant F is needed because at the time of Nernst's writing (and also this posting I suppose) the ampere was used in the SI system, so electrical potential energy was still being measured in J/C rather than J/Eq. The z relates moles of charge to moles of ions. But it is the ions which are being counted as they pass through the membrane, and which are subject to a Boltzmann distribution: E = K e^(-RT). Note the striking aspect that there is hypothetically infinite energy available when one concentration is zero, as we start with here, because given enough time the channel at a finite temperature will allow a single ion to pass through into an empty space against any potential difference whatsoever. Writing that in terms of information should be interesting.

The channels make it possible to set an equilibrium between an electrical potential on the membrane and the energy encoded (?) in the "information" of the particle. I doubt that this is simply which side of the membrane it is on, but perhaps it has to do with how well you can localize its position in space on one side or the other?

Although the ions are in water, they act much like a gas of particles (right down to the quantity of osmotic or gas pressure they would apply to a membrane). So I'm hoping the answers here also give a yes or no to Alicki's statement that "gas of atoms may possesses a well-defined entropy but does not encode any information".

 

[eljose79]

I appreciate your interest in understanding the concept of information in physics. Robert Alicki's paper is an interesting read and raises important questions about the relationship between information and physical systems. It is important to note that while Alicki's paper has not been published in a peer-reviewed journal, it has been cited and discussed by other scientists in the field, indicating its significance.

One of the key points in Alicki's paper is that information is not a physical property, but rather a result of our interpretation and understanding of physical systems. This idea challenges the traditional view that information is a fundamental aspect of the physical world. However, it does not necessarily mean that information is not important in understanding physical systems. In fact, many scientists are now exploring the role of information in various physical phenomena, such as entropy and thermodynamics.

Regarding your example of the cell membrane, the concept of information can be applied in understanding the behavior of ions and channels. The opening and closing of channels can be seen as a transfer of information, as it controls the movement of ions and ultimately affects the equilibrium of the system. The process of ion movement can also be described in terms of information, as it involves the exchange of energy and information between the ions and the membrane.

In terms of Alicki's statement about a gas of atoms not encoding any information, it is important to clarify that this may not be entirely true. While a gas of atoms may not possess a well-defined entropy, the behavior of the particles can still be described in terms of information. For example, the positions and velocities of the particles can be seen as encoding information about the state of the system.

Overall, the concept of information in physics is an ongoing area of research and there are still many open questions. I encourage you to continue exploring this topic and considering different perspectives, as it can lead to a deeper understanding of physical systems.