Where physics meets biology: More information

The article by Paul Davies (Physics Today, August 2020, page 34 ) addresses the importance of information theory in biological systems. As pointed out by Erwin Schrödinger, biological systems gain negative entropy from food and have tremendously less entropy than physical or thermodynamical systems.

Let me quantify that statement. Claude Shannon showed that the entropy in information theory is related to a thermodynamical system through $-k_{\mathrm{B}}N\ln p$, where $k_{\mathrm{B}}$ is the Boltzmann constant, $p$ is the probability of a given state, and $N$ is the state’s number of degrees of freedom. ¹ The fact that a biological system has huge negative entropy can be explained simply by considering $N$.

If a DNA molecule acts as one unit of a degree of freedom, as it should, the entropy of a human body is about 12 orders of magnitude smaller than that of a system having free molecules in equilibrium at the same temperature, since the molecular weight of a DNA molecule is approximately a trillion times that of, say, a water molecule. That is, human cells are better ordered by a huge factor (10¹²) than is a system in thermodynamic equilibrium.

That factor allows the human system to work with a thermal efficiency much higher than a supercomputer’s. In a chess game between a person and a supercomputer, for example, the energy efficiencies differ by about six orders of magnitude. A human brain weighs about one-millionth of what a supercomputer does; thus the efficiency per unit weight of a human brain can be 1 trillion times greater, in agreement with the amount of negative entropy of the human cell system.

Since the molecular weight of human DNA is not much different from that in other living cells, a similar argument applies to most living systems. Most other animals do not play chess, but the amount of information processed in their visual and other sensory systems can be similar in magnitude to the human brain’s processing capacity. Furthermore, I would say that life is a process of maintaining the system’s huge negative entropy through cell division (reconstruction of a cell) and autophagy, while disease and death arise in the gradual and sudden increase of internal entropy or loss of negative entropy.