Sunday, September 16, 2012

Disproving a Heat Death to the Universe


There have been the claims by lots of famous chemists and physicists that there will be an eventual “Heat Death of the Universe.” In fact, the whole idea of a heat death of the universe has generated an entire philosophy of life called the Thermodynamic Imperative. In a previous posts, I've pointed out that there is an irrational fear in parts of our society regarding entropy production. One way of stating the Thermodynamic Imperative is the following: "Waste not useful potential energy." I couldn't agree more with this statement. I think that we should be using useful potential energy to help grow life. The problem is that there are some people in the scientific-environmental community (such as Nicholas Georgescu-Roegen) who have taken the Thermodynamic Imperative to the extreme and have taken it to mean that we should minimize the production of entropy at all costs and we should do this by promoting a philosophy of de-growth. Before I delve into the problems with the philosophy of de-growth, I'd like to go back to one of the original statements regarding the heat death of the universe.

In 1862, Lord Kelvin (William Thomson) wrote the following regarding the implications of the second law of thermodynamics:

"The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws. But it is impossible to conceive a limit to the extent of matter in the universe; and therefore science points rather to an endless progress, through an endless space, of action involving the transformation of potential energy into palpable motion and hence into heat, than to a single finite mechanism, running down like a clock, and stopping forever."

So, even from the beginning, Lord Kelvin was aware of the implication of the second law of thermodynamics, but was smart enough to realize that whether we reach a heat death depends entirely on whether the universe is finite and whether it is growing in size. Lord Kelvin was spot on when he stated that science points to "endless progress" (emphasize is mine.)

If the universe were finite in size, then the idea of a heat death to the universe makes sense. However, if the size of the universe were to increase as entropy increases, then there would never be a true heat death. The average energy density in the universe would decrease, but the universe could continue to increase in entropy because there would continue to be the capability to do useful work because there would still be gradients in temperature and chemical composition.


It's easier to think about the idea of heat death by using the concept of exergy. The molar exergy of an ideal gas with constant specific heat entering a control volume is equal to

Where T is the temperature of the gas, p is the partial pressure of the gas, To is the temperature of the reference environment, and po is the partial pressure of the gas in the reference environment.
What we can see is that the value of the exergy depends critically on what is the value of the temperature and the pressure of the reference environment.

There is a similar equation for the exergy within a control volume for a gas with specific constant heat:

 As the universe expands, the reference temperature and the reference partial pressure of the environment is decreasing. You can use this equation to estimate the exergy of a gas in a control volume as a function of the temperature and pressure of the reference environment. What you'll find is that the exergy will remain above zero as long as the partial pressure and the temperature of the gas in the control volume is decreasing slower than the partial pressure and the temperature of the reference environment. When does the exergy go to zero? Only when the partial pressure and the temperature of the reference environment is exactly equal to the partial pressure and temperature of the gas in the control volume.

So, even if the average temperature of the matter in the universe decreases, this does not imply a heat death to the universe if the universe continues to expand.  It has been recently suggested that the expansion of the universe is entirely due to the increase in entropy within the universe. This means that as the entropy of the universe increases, the surface area of the universe increases. So, while it may be that the average temperature of the universe will decrease with time, this does not imply a heat death to the universe.  (Note that temperature is defined as the derivative of total energy with respect to entropy...i.e. it is similar to a ratio of the total energy to the total entropy. Since the energy of the universe remains constant and the entropy is increasing, then the average temperature of the universe will necessarily decrease with time. Time is necessarily defined with respect to the increase in the surface area of the universe due to irreversible entropy production. Note also that temperature and entropy can be defined for systems not-in-equilibrium because entropy is the logarithm of the exchange symmetries between particles and can be defined for systems not-in-equilibrium.) In other words, increasing the entropy of the universe is the same as increasing the size of the universe and increasing the exchange symmetries between equivalent microstates. Increasing entropy is not a bad thing at all because it increases the size of the universe and increases the symmetry group of the universe. That's pretty cool! The natural dissipative processes of the universe (both by living agents and by non-living processes) increase the symmetry group of the universe and increase the size of the universe.

So, life can increase the symmetry of universe, but this does not necessarily mean that we will run out of exergy. In fact, as we get to lower temperatures, we know that we can use superconducting wires and superfluid helium in our power plants in order to generate useful work even as the average temperature of the universe decreases to the range of a few Kelvin. (Which is not expected to happen for a long, long time.) Intelligent life should be able to live off of gradients in temperature and chemical composition even as the temperature of the universe drops to below 1 Kelvin.

So, we could imagine a growing and thriving civilization even if the temperature of the universe is less than 1 Kelvin. This would not be a human form of life, but perhaps future life forms could design self-replicating robots that could grow and survive off of gradients in temperature and chemical composition even if the temperature is really cold. The reason that we can do this is that cold is a relative definition. When you have a logarithm term, the difference between 0.1 Kelvin and 1 K is the same as the difference between 100 K (really cold to us) and 1000 K (really hot to us.)

So, if there is an virtually endless supply of exergy in the universe (though possible finite), this means that there is no need to “conserve” exergy and save it for future generations. As stated earlier, there are some people who believe that the goal of life is to use as little exergy as possible. This is just silly. The exergy of the universe is extremely large and the exergy will not go to zero as long as there are gradients of temperature and chemical composition, which seems possible because the size of the universe is not fixed.

But regardless of whether the amount of exergy is finite, the main reason why the philosophy of de-growth is silly is that there are natural processes that destroy exergy. There’s no way to stop the natural forces of exergy destruction. Stars will continue to burn hydrogen regardless of whether you think you should “conserve exergy.” De-growth will not prevent entropy production via natural processes.
When natural processes destroy exergy (via irreversible processes), the size of the universe increases, and the reference partial pressures and temperature of the universe decreases. So, it’s not like the natural processes are bad. As they generate entropy, the universe expands and what we should take as the reference partial pressure and reference temperature decreases…increasing the exergy of a gas inside a control volume.
In other words, the concept of exergy should only be used where it’s applicable. The concept of exergy should not be construed as some reason to promote the philosophy of de-growth. The concept of exergy is only useful when there's a system in which the reference partial pressures and temperature is not changing with time. In this case, you can say that exergy is destroyed by irreversible processes. But the exergy is destroyed only with respect to the partial pressure and temperature of that particular environment.  As stated in the Guoy-Stouda equation for exegy destruction (i.e. exergy destruction is equal to the temperature of the reference environment times the production of entropy via irreversible processes), if the temperature of the reference environment is zero, then there is no exergy destruction. This is the other reason why it's silly to think that we should avoid exergy destruction: "exergy destruction is zero if the temperature of the universe is zero." We are only destroying exergy with respect to the Earth's pressure, temperature and chemical composition, not with respect to empty, cold space.

So, in summary, it’s true that generating entropy via irreversible processes will eventually lead to a universe in which there are more exchange symmetries between particles (i.e. more uncertainty in the exact microstates of the universe.) And it’s true that the average energy density and the average temperature of the universe will decrease with time. However, there is no ‘moral imperative’ to cut back on our entropy production (i.e. exergy consumption) because the exergy of the universe is not fixed. The total amount of exergy available depends on the temperature and partial pressure of the reference environment.


The 'moral imperative' is to grow life because this is the best way of increasing the entropy of the universe (and hence increasing the size and the symmetry group of the universe.) We should consume useful potential work to help find more useful potential work. This is what life does. Life self-replicates and grows. It uses stored potential work to make copies of itself so that those copies can find stored work and make more copies. This is a good thing! The process of self-replication can continue for virtually an endless amount of time (likely even at temperatures below 1 Kelvin.) The smarter we become, the more likely we will be able to develop technologies that can grow life even as the average temperature decreases. Therefore, the underlying anti-growth philosophy in academia has no scientific basis. In fact, the moral imperative is not to 'conserve exergy,' but to 'use gradients in temperature and chemical composition to grow life.'

In other words, ethics is real and it can't be reduced to "Do whatever you want," "Do what is natural" or "Do what God tells you to do." Ethics is real, but the formulation of societal laws to promote ethical behavior will necessarily be complicated because growing life is complicated. There's no set rules on how to grow life. There's no formula on how to grow life the best because we can't predict the future. The laws of society should change as we learn more about the world, but this does not mean that ethics is relative. Ethics is absolute (i.e. Grow Life); it's just that the laws that promote ethical behavior are imperfect. Even the most fundamental law of society (don't kill) is imperfect because there are grey areas (self-defense and war.) (Try imagining a world in which lions don't kill gazelle or whales don't eat krill.) My hope is that intelligent human life forms start growing life on other planets so that we can remove the faulty idea that all life depends on the death of some other life form. We can grow life on other planets and in other solar systems, and therefore, we are not constrained by the finite size of the Earth or the finite amount of hydrogen in the Sun. The only constraint to growth is a lack of innovation. If we continue to innovate, life will be able to grow for a virtually endless amount of time.

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