# Information Theory and Computational Thermodynamics: Lessons for Biology from Physics

## Abstract

**:**

## 1. Unifying Information and Energy through Computation

_{2})kT (where k is Boltzmann’s constant, and T the temperature of the system).

**Figure 1.**The logical gate and is not reversible as can be seen in this truth table diagram, because given 0 as output one cannot tell which of the 3 inputs generated it.

_{2})kT every time M bits are erased. We have a good sense of how to connect these concepts using algorithmic information theory. If a string is algorithmically random, for example, there is no way the machine can be set up to make it produce usable work, because the more predictable the string (the lower its algorithmic—Kolmogorov—complexity [13,14]) the more the quantity of work that can be extracted from it. This is consistent with the second law of thermodynamics—computational thermodynamics basically says that one cannot extract work from an (algorithmically) random string. The machine would either not be able to fully predict the incoming input or it would require more energy to actually predict its bits and prepare itself to take advantage of the incoming input and produce work. In the words of Feynman ([8]), a random tape has zero fuel value.

**Figure 2.**A bit for work regarded as a particle pushing the piston if it is known whether the bit will be 1 or 0 (interpreted as coming from one direction or the other). Every bit in the sequence determines whether the piston will expand one way or the other, but in order to do so the piston has to be in the right position.

#### 1.1. Thermodynamics, Computation and Computability

## 2. The Role of Information in Physics

It is tempting to take the limit where the surface area goes to infinity, and the surface is locally approximately at. Our variables on the surface then apparently determine all physical events at one side (the black hole side) of the surface. But since the entropy of a black hole also refers to all physical fields outside the horizon the same degrees of freedom determine what happens at this side. Apparently one must conclude that a two-dimensional surface drawn in a three-space can contain all information concerning the entire three-[dimensional] space. ... This suggests that physical degrees of freedom in three-space are not independent but, if considered at Planckian scale, they must be infinitely correlated.

^{−33}cm and ∼ 10

^{−43}s) at which general relativity breaks down and should be replaced by laws of “quantum gravity” (Wheeler is also credited with having coined the terms Planck time and Planck length). Wheeler [24] thought that quantum mechanics would eventually be rooted in the “language of bits”. According to [25], Wheeler’s last blackboard contained the following, among several other ideas: “We will first understand how simple the universe is when we recognize how strange it is.” Wheeler himself provides examples of the trend from physics to information in his “it from bit” programme, suggesting that all of reality derives its existence from information. He asserted that any formula with units involving the Planck length ħ would be indisputable evidence of the discrete nature of the world. It was perhaps not by chance that the same person who coined the term “black hole” for the strange solutions that general relativity produced, leading to singularities, proposed the “it from bit” dictum, suggesting that everything could be written in, and ultimately consisted of, bits of information.

## 3. Information and Biology

**Figure 3.**A step configuration of Conway’s Game of Life [41] (each cell looks to its neighbours to stay alive or die—stay black or white). Surprisingly, simple processes like this rule system, today called a cellular automaton, can capture fundamental aspects of life such as self-assembly, robustness and self-replication, and are capable of the most important feature of computation: Turing universality. von Neumann [40] sought to model one of the most basic life processes—reproduction—by designing these kinds of lattice-based rules where space is updated altogether in discrete steps for studying self-replication.

#### 3.1. Computational Thermodynamics and Biology

^{11}kT per discharge [4]. Computers (mainly because of their volatile memory devices—the RAM memory) also dissipate energy by at least 1kT per bit [3,4], which is also the reason computers heat up and require an internal fan.

## 4. Concluding Remarks

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Zenil, H.
Information Theory and Computational Thermodynamics: Lessons for Biology from Physics. *Information* **2012**, *3*, 739-750.
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Zenil H.
Information Theory and Computational Thermodynamics: Lessons for Biology from Physics. *Information*. 2012; 3(4):739-750.
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**Chicago/Turabian Style**

Zenil, Hector.
2012. "Information Theory and Computational Thermodynamics: Lessons for Biology from Physics" *Information* 3, no. 4: 739-750.
https://doi.org/10.3390/info3040739