Schrodinger entropy and free energy

In 1944 the physicist Erwin Schrodinger published a short book entitled What is life? (I have referred to the slightly amended 1948 edition for reasons which will become apparent.) This book was influential in attracting many young physicists to biological problems in the mid-twentieth century (Perutz, 1987), and indeed Gould (1995) considered it amongst the 'most important books in 20th century biology', while Paul Davies (2005) has emphasized the irony that 'one of the most influential physics books of the twentieth century was actually about biology'.

Box 2.1: Entropy and information

The principle sources for my approach in this box are Lovelock (2000a) and Penrose (2004).

Entropy (s) is the measure of the disorder of a system and is a notoriously difficult concept.

Formally:

where K = Boltzmann's constant (1.38 X 10~23 JKT1), and P = a measure of disorder, effectively a measure of probability or the 'degree of surprise' (Aleksander, 2002).

Life is 'surprising' and as such has low probability (P) and hence low entropy (s). The idea of entropy is closely related to Claude Shannon's concept of information. Indeed information can be defined as 1/s. Entropy can roughly be thought of as a measure of 'randomness' in a system whereas information can be thought of as a certain kind of lack of randomness.

A more formal definition of entropy requires the concepts of 'phase space' and 'coarse graining' (see Penrose 2004, chapter 27). However, for the arguments developed in this book all that is required is an understanding of the reciprocal relationship between entropy and information and a 'feel' for entropy as a measure of randomness (or negative entropy as a measure of surprise).

Although many of its more original ideas turned out to be wrong, it was influential in a way that defies simple summary (see discussions by Gould (1995) and Perutz (1987)).

In his book Schrodinger (1948, p. 71) famously described the process by which an organism survives as continually drawing negative entropy from the environment. In fact on thermodynamical considerations this is not strictly true, as pointed out by Franz Simon soon after the book was first published. In the 1948 edition of his book Schrodinger added a note to this effect, admitting that it might be better to consider organisms as drawing on free energy rather than negative entropy. These niceties of thermodynamic theory are not crucial for the concerns of this book. However, what Schrodinger was describing in thermodynamic terms is an important concept in ecology; namely that to survive all organisms must acquire energy from their environment and in so doing produce waste products which they release back into their surroundings. Indeed this is so fundamental that it could be considered the basic concept of ecology.

Schrodinger, entropy, and free energy 19

To a (very) naive physicist, organisms appear to break the second law; however, they are not closed systems as they draw free energy from their surroundings, this is what enables them to give the illusion of cheating the second law. Just as a domestic refrigerator appears to violate the second law by moving heat from a cold to a hotter body, if the whole system is considered (in this example the refrigerator and its environment, which includes processes in the power station supplying the electricity) there is still a global increase in entropy although entropy decreases locally within the refrigerator. In a thermodynamic context the whole Earth system can be viewed in a similar way to an organism, for example Lenton (2004) described Gaia as 'a type of planetary-scale, open thermodynamic system, with abundant life supported by a flux of free energy from a nearby star'. In this respect it is sensible to consider Gaia as a superorganism, and the analogy is useful if one is considering energy (or entropy). However, clearly Gaia does not have 'genetics', so while a classical biochemist (interested in metabolism) could find merit in viewing the whole Earth System as a giant organism, a molecular biologist (interested in questions of information and genetics) would not. Like most metaphors, the idea that 'the Earth is alive' is useful in thinking about some questions but misleading for others. It is no doubt relevant that James Lovelock's background is as a chemist who worked for many years in medical research, prior to the great expansion of molecular biology, indeed he is happy to describe himself as 'an old fashioned organic chemist' (Lovelock, pers. comm.). However, many of the most important applied problems in the environmental sciences are essentially ones of the Earth's metabolism, for example changes in the carbon cycle. For these problems the metaphor of the living Earth has some merit.

Schrodinger's point about organisms and thermodynamics can be simply characterized as

Energy ^ organism ^ waste product

This is clearly very similar to the food chains common in introductory ecology texts, for example:

Solar energy ^ green plant ^ herbivore ^ carnivore

However, in classical descriptions of food chains and food webs many of the waste products (CO2, O2, heat, etc.) are never shown, and many others (e.g. faeces or dead leaves) are only shown in special cases (Box 2.2). As no real system can be 100% efficient, any organism using free energy from its environment must be producing waste, which is then released back into the environment. As such there is nothing special in the fact that humans cause pollution (i.e. add waste to their environment), what is different about us is the size of the effect. Within my lifetime (I was born in 1963) the human population has more than doubled (Cohen, 1995), and in addition an increasingly affluent and industrial world is producing ever more waste. For example in 1990 there were approximately 478

Box 2.2: Illustrations of the partial nature of most food webs

Here I briefly describe three food webs from different environments (terrestrial, freshwater, and estuarine) to illustrate the poor coverage of decomposers such as bacteria, protozoa, and fungi, in most food webs. Waste products are often ignored yet provide the free energy for crucial guilds of organisms (e.g. microbes involved in decomposition). For a recent, and rare, example of a detrital soil food web, see Mulder et al. (2005).

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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