A short essay on the differences between the thermodynamic definitions and our intuitive notions of entropy and disorder.
'Everything that can possibly go wrong will go wrong' is a popular adage often dubbed as the Murphy's law. When we observe the world around us, disorder seems to be all pervasive. Untidy shelves, messy rooms, violent protests, and the tempestuous state of world politics in general are considered to be day-to-day manifestations of the law of disorder. In common usage, the definitions of disorder, randomness and entropy are used interchangeably, and this leads to numerous misconceptions in thermodynamics, and its application to other fields. In pop-culture, Murphy’s law has often been confused with a law of thermodynamics. Some say it is the 4th law; which is totally misplaced and an utterly erroneous claim.
The common definition of “entropy” as the measure of disorder or randomness of a system is invoked by the creationists in support of their claims against evolution. Their assertion is that in the light of the law of disorder (often confused with the Second law of thermodynamics), it is impossible for the process of evolution to spontaneously create life, the building block of which is based on a highly ordered structure of the gene. If the universe is creating more disorder with each passing second, the evolution of life is impossible – this is a hasty conclusion creationists draw, deeply rooted in an incomplete and erroneous understanding of entropy and what the Second law of thermodynamics states about it. For the sake of argument, even if “entropy” were synonymous with “disorder”, the second law would still not contradict evolution. This is explained by the fact that entropy, or disorder for the sake of this argument, strictly increases only in an isolated system. Isolated systems are an abstraction and do not exist in nature. The primordial soup where the life is supposed to have emerged from, and the subsequent ecosystems which supported the diverse life forms are nowhere close to being thermodynamically isolated. Hence the claim of invalidity of the evolution falls flat in the light of the Second law, even if we assume disorder and entropy to be analogous.
It has been established so far that the entropy of a non-isolated thermodynamic system like the earth does not necessarily increase. Are genes, then, simply the expressions of thermodynamic order? Can we extend the thermodynamic definition of entropy to assert that a gene, which is a definite (ordered, if you will) sequence of nucleotides, is a product of the process characterized by a decrease in entropy? Also, does thermodynamic concept of entropy apply to our rooms which tend to a state of disorder when left alone? What is entropy? Is it simply a measure of how unorganized and haphazard a system can be? Let us delve right into it!
Classical Thermodynamics deals with the statistical predictions of the collective motion of particles (macrostate) from their microscopic behavior (microstate). A macrostate is an emergent state of a thermodynamic system, described by the properties like pressure, temperature, density etc. while as a microstate is a specific configuration that the microscopic constituents of a thermodynamic system may exist in with a certain probability. The Second law of thermodynamics and the concept of entropy strictly apply to the systems in equilibrium. Thermodynamic equilibrium is an axiomatic concept which describes the state of a system as the one with no net macroscopic flow of energy or matter either within the system or between the systems. Consider an insulated bottle of 1 liter volume. Given that the bottle is insulated, there is no exchange of energy or matter between the bottle and its surroundings. Under the standard atmospheric conditions, the number of molecules contained within the bottle are approximately of the order of \(10^{22}\). The position and velocity of the individual molecules is changing with respect to time and each different configuration of the molecules inside the bottle corresponds to a microstate. The caveats to be followed while trying to compute the number of microstates are \(1)\) that the molecules are not allowed to lie outside the volume of the bottle; \(2)\) that in each microstate the sum of energies of individual molecules has to be equal to the total energy of the gas, and of course; \(3)\) the total number of molecules inside the bottle has to be fixed. What is interesting is that a small change in the position or velocity of a molecule changes the whole configuration of the gas inside the bottle and thus yields a new microstate. Now imagine in how many ways can a system of \(10^{22}\) molecules be arranged! \((\)by slightly changing the position and velocity of each molecule while satisfying \(1), 2)\) and \(3))\) This number is huge, try calculating it! The number of such arrangements is loosely termed as “disorder” in thermodynamic jargon. This number will be denoted by a letter ‘\(\omega \)’ elsewhere in the text. The idea of association of the thermodynamic definition of disorder to that of the pop science is outright delusional. The number of microstates ‘\(\omega \)’ does not point to a common state of disorderliness or messiness (of our rooms), the one that pop-science writers mistakenly identify it with.
The equation that relates the thermodynamic concept of disorder ‘ω’ with the entropy was for the first time written down by one of my favorite 19th century scientists, Ludwig Boltzmann. It reads,
\[ S=k_B ln(\omega) \ \ \ \ \ (Boltzmann \ Entropy \ Equation)\]
Where \(S\) represents the entropy associated with the system, given that \( \omega \) number of microstates exist. \(k_B\) is the Boltzmann constant.
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| Boltzmann's grave in the Zentralfriedhof, Vienna, with bust and entropy formula. Source: Daderot/Wikipedia |
Classical thermodynamics confines itself to the systems in dynamic equilibrium, as already explained. In relation to the idea of thermodynamic disorder, the implications of the axiomatic concept of equilibrium are that all these microstates are equally probable, randomized and representatives of the same macrostate. In our bottle example, the snapshots of the molecules separated by any random interval of time will be different while as the macrostate of the gas/fluid inside the bottle measured by pressure, temperature and other macroscopic properties stays the same.
Now, let us try to apply these concepts to measure the ‘disorder’ of a room. If you have nothing better to do on a weekend, sit quietly and observe your room for hours. Clearly, it is possible to arrange the items present in the room in many ways and hence many configurations of the constituents of the room are possible. However, what you will notice is that the condition of the room pretty much stays the same and no spontaneous randomization of the different microstates of the room occurs. The state your room is in, is the most probable state – a microstate. To compute the thermodynamic disorder ω, a system must have a finite number of equally probable microstates which are randomized between measurements. In the case of our room example, only one, single completely specified state exists, and an ensemble of such states that is essential in computing its entropy does not exist. Hence the idea of thermodynamic entropy applied to messy rooms and shelves is flawed and ridden with all the misleading attributes of pop-science.
Let us extend these concepts to the ordered sequences of nucleotides – the genes. For the sake of clarity, let us make up a 15 letter sample gene with the following sequence of imaginary nucleotides,
\[ SuperGene = ABCDEFGHIJKLMNO \ \ \ \ \ (biologically \ functional) \]
Creationists’ claim would be that the existence of SuperGene as the only possible functional arrangement of nucleotides owing to its unique order among the total of \(15! = 1307674368000\) (repetition of letters not allowed) sequences of nucleotides, \(15! - 1 = 1307674367999\) of which are random and biologically non-functional, is a violation of the Second law of thermodynamics. But think about it, the macrostate is not to be confused with a particular gene, rather it is an ensemble of all the \(15!\) genes, were they randomized and equally probable. It is futile to talk about the order or thermodynamic entropy of a particular gene, say SuperGene or any other random permutation, because of the reason that it is just one of the possible configurations of the sample nucleotides and not a macrostate. Unless we excite the SuperGene by supplying energy and break the chain of nucleotides, it is going to remain as it is. Such is the case with all other combinations. As long as a particular gene is stable and exists indefinitely, our measurements of looking at them are not randomized and it makes no sense to apply the standard definition of thermodynamic entropy which assumes that the microstates be randomized with vanishingly small but equal probabilities. However, in the case of our messy room and gene examples, there exists a single configuration of the constituents with a near unity probability of observing that configuration, which is not in accordance with the foundations of the Second law. Therefore, the claim that the Second law of thermodynamics forbids and prevents the self-assembly of the information (DNA) necessary for life is absurd and grossly misplaced.
The idea of order, disorder, and entropy in thermodynamics and our intuitive notions of these words are entirely different. In future, if you happen to read a misleading pop-science article that dabbles in the terminology of thermodynamics and cites famous aphorisms associating disorder and thermodynamic entropy, you know what to do!
Cite as
Bader, Shujaut H., “Entropy and disorder: from genes to messy rooms, A short essay on the differences between the thermodynamic definitions and our intuitive notions of entropy and disorder.” Backscatter, August 2, 2020, https://backscatterblog.blogspot.com/2020/08/entropy-and-disorder-from-genes-to.html.
References
- The Laws of Thermodynamics, A Very Short Introduction, Peter Atkins.
- Statistical Physics of Biomolecules, An Introduction, Daniel Zuckerman.
- Thermodynamics, Evolution and Creationism: Entropy, Disorder and Life, John Pieper, The TalkOrigins Archive.
- Statistical Physics, Third Edition, Part 1: Volume 5 (Course of Theoretical Physics, Volume 5), L D Landau, E.M. Lifshitz.
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