The Information Catastrophe

We now explore these implications from the point of view that a bit of information is not just an abstract mathematical entity, but it is physical. In 1961, Rolf Landauer first proposed a link between thermodynamics and information. Landauer predicted that erasing a bit of information requires a dissipation of energy, equal to at least k

_B

T · ln(2), where k

_B

is the Boltzmann constant and T is the temperature at which the information is stored.

²2. R. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. Res. Dev. 5(3), 183–191 (1961). https://doi.org/10.1147/rd.53.0183

Due to the conservation of energy, an energy input of the same value, k

_B

T · ln(2), is required to create a bit of information. This is known as Landauer’s principle,

³3. R. Landauer, “The physical nature of information,” Phys. Lett. A 217(4-5), 188–193 (1996). https://doi.org/10.1016/0375-9601(96)00453-7

deduced from thermodynamic considerations and demonstrated experimentally in several recent studies.

^4–74. J. Hong, B. Lambson, S. Dhuey, and J. Bokor, “Experimental test of Landauer’s principle in single-bit operations on nanomagnetic memory bits,” Sci. Adv. 2(3), e1501492 (2016). https://doi.org/10.1126/sciadv.15014925. R. Gaudenzi, E. Burzurí, S. Maegawa, H. S. J. van der Zant, and F. Luis, “Quantum Landauer erasure with a molecular nanomagnet,” Nat. Phys. 14, 565–568 (2018). https://doi.org/10.1038/s41567-018-0070-76. A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of Landauer’s principle linking information and thermodynamics,” Nature 483, 187–189 (2012). https://doi.org/10.1038/nature108727. Y. Jun, M. Gavrilov, and J. Bechhoefer, “High-precision test of Landauer’s principle in a feedback trap,” Phys. Rev. Lett. 113(19), 190601 (2014). https://doi.org/10.1103/physrevlett.113.190601

Here, we estimate the energy and power needs to sustain the annual production of information assuming an annual growth of f% per year. Currently, the energy required to write a bit of information, regardless of the data storage technology used, is much higher than the minimum predicted energy, Q

_bit

= k

_B

T · ln(2) ≈ 18 meV at room temperature (T = 300 K). Let us assume that our future technological progress will allow writing digital information with maximum efficiency. In this case, the total energy necessary to create all the digital information in a given n-th year, assuming f% year-on-year growth, is given by

$Qinfo(nth)=Nb\cdot kBT\cdot ln(2)\cdot f+1n.$

(2)

The total planetary power requirement to sustain the digital information production is obtained dividing relation

(2)

by the number of seconds in a year, t ≈ 3.154 × 10

⁷

.

Figure 2

shows the annual power vs number of years in the logarithmic scale for f = 1%, 5%, 20%, and 50%, respectively. The total power requirement today to power all industries, transportation, and domestic energy needs on Earth is around 18.5 × 10

¹⁵

W = 18.5 TW,

⁹9. International Energy Agency, Key World Energy Statistics 2019 (International Energy Agency, 2019), pp. 6–36.

i.e., in logarithmic value, this is log

₁₀

(18.5 × 10

¹⁵

) = 16.27. As seen from

Fig. 2

, for 1% growth rate, after ∼5200 years, the creation of digital content will take up the equivalent of all today’s planetary power requirements. Similarly, for 5%, 20%, and 50% growth rates, this will occur after ∼1060, ∼285, and ∼130 years from now, respectively. It is worth reminding that these estimates have assumed production of digital content at the maximum efficiency, which is certainly not the case yet. Hence, it appears that the current growth rate is unsustainable and digital information production will be limited in the future by the planetary power constraints. This limitation could be formulated in terms of entropy, as introduced by Deutscher in his book, The Entropy Crisis, in which he argues that the energy crisis is, in fact, an entropy crisis because the entropy increase in the biosphere requires energy.

¹⁰10. G. Deutscher, The Entropy Crisis (World Scientific, Hackensack, NJ, USA, 2008).

Since information production actually increases the entropy of a system, by extrapolation, producing digital information also increases the entropy of the biosphere. Interestingly, this increase in the information entropy of the biosphere could be used in reverse, to harvest energy from entropy as previously proposed.

¹¹11. E. Bormashenko, “Entropy harvesting,” Entropy 15, 2210–2217 (2013). https://doi.org/10.3390/e15062210

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