Open and Closed Systems: Know Your Boundaries

The concept of open and closed systems does not, at first glance, fire up the imagination as say, interstellar travel, but as we will find out, not knowing the difference between the two is the source of some popular misconceptions.  A closed system is one whose boundaries are impermeable.  An open system is the opposite with flows going in and out of the boundaries.  Below, we’ll take a look at examples from physics and economics to see why this is an important distinction.

I have often seen arguments that evolution theory is a violation of the 2nd law of thermodynamics.  Before I get into that, lets review a couple of key points on thermodynamics.

Energy will transfer from a warm region to a cooler region.  That is, if an object is 100 degrees and is placed in a 70 degree room, the object’s heat will transfer to the cooler room until they are both the same temperature.

The 2nd law of thermodynamics states that in a closed system, entropy increases.  A closed system is one where no energy leaves or enters the system.  Increasing entropy is a fancy way of stating that an ordered system becomes more disordered over time.  This is a result of the possible disordered states being far more numerous than possible ordered states.  Think of a deck of cards.  When we pull the cards right after we purchase the deck, the cards are in numerical and suite order.  This ordered state is one of a possible 8 x 1067 combinations for a deck of cards.  The remaining combinations are disordered to some extent.  If the cards drop off a table to the floor, the probability they will be ordered randomly is much greater than retaining their original order.  The same is true of an egg on the table that drops to the floor.  In fact, this is the only law in physics that provides a direction for time in the manner of irreversible processes – that egg is not going to reassemble itself back into its shell.

The argument against evolution claims that as the Earth has progressed through time, entropy has decreased as more and more complex life forms have evolved.  The problem here, Earth is not a closed system in that it continuously receives energy from the Sun.  That energy is available to perform work on Earth to create order from disorder.  For example, energy from the Sun is stored in food that is consumed by a person who uses that energy to put the deck of cards back in order.  The Sun becomes more disordered in the process than the deck of cards gains order.  Think of all the energy the Sun releases that does not even reach the Earth and is lost to the rest of the universe.  Hence, the evolution of complex life on Earth results in net disorder overall in the Earth-Sun system and the universe as a whole.  The 2nd law of thermodynamics is not violated by evolution.

The HMS Beagle in the Straits of Magellan in 1890. On board was Charles Darwin to study evolution of life in the Galapagos islands. Credit: Wiki Commons.

In terms of equations, the increase in entropy as heat is transferred from a hot reservoir (Sun) to a cold reservoir (Earth) can be stated as follows:

ΔS = Q/Tc – Q/Th where:

S = entropy, Q = heat (Joules), T = temperature (Kelvins)

We’ll take a simplified example of a 100% efficient heat transfer from a hot to cold reservoir and set Q = 1,000 J, Th = 2,000 K, and Tc = 1,000 K.

ΔS = 1,000J/1,000 K – 1,000J/2,000 K = 1/2 J/K

As Q/Tc is always greater than Q/Th, entropy (disorder) always increases.

Our lifetimes on Earth are pretty small compared to the cosmic timescale and it’s difficult to think of the Sun becoming more disordered.  But if we fast forward time by about five billion years, the Sun which looks quite ordered today:

Credit: SDO/NASA

Will become a disordered planetary nebula that looks something like this:

NGC 6751, Credit: James Long & the ESA/ESO/NASA

Could the Sun-Earth system receive energy from an outside source?  In the case of a nearby supernova, yes.  The Sun itself is a 2nd generation star created from the remnants of a prior supernova.  The shock from the supernova imparts energy in the form of angular momentum on a nebula, causing it to flatten and begin the create a star and planetary system.  In that case, the supernova is a highly disordered state:

Tycho’s Supernova Remnant, Credit: NASA/CXC/GSFC/B.Williams et al; Optical: DSS

That imparts just a tiny, tiny fraction of its disordered energy to create an ordered protoplanetary disk such as this:

Protoplanetary Disk of HL Tauri, gaps are where planets are forming. Credit: ALMA (ESO/NAOJ/NRAO), NSF

The universe is a closed system that began as a highly ordered state at the Big Bang and has become more and more disordered throughout time.  What is the endgame for the universe?  All evidence points towards heat death, a state where the entire universe is the same temperature (absolute zero) and all physical/life processes cease.  Worry not, that will be many, many billions of years in the future.

Heat death of the universe symbolized in Camille Flammarion’s 1893 novel The End of the World.

Could the universe itself be an open system?  Only if energy somehow leaked in from another universe present in an overall multiverse.  However, to date, no known such process has been observed.  Thermodynamics has proven to be a remarkably sturdy holdover from classical 19th Century physics.

In economics, confusion over open and closed systems presents one of the great misconceptions on how to mitigate recessions.

During a recessionary period, the government can respond in one of two ways to alleviate the downward trend.  One is monetary policy to reduce interest rates, the other is fiscal policy to expand government spending.  The latter is often rebutted by political opponents using the household example.  The argument being that if a household income declines, the proper response is to tighten the belt rather than increase spending.  The problem with that argument is this:

A household is an open system.  Income flows in from an employer/business outside the household.  Spending and savings also flows out of the household towards businesses and financial institutions.  Thus, it is quite possible for a household to say, increase income by working longer hours and reduce spending simultaneously to make ends meet.  A national economy works differently.

A nation’s gross domestic product (GDP) is defined as follows:

Consumption + Investment + Government + Exports – Imports

or

C + I + G  + (X – M)

Imports are subtracted as it is already included in consumption and this avoids double addition.  Unlike a household, a national economy is a closed system.  Spending does not flow outside the system boundaries.  Your income is a result of someone else’s spending.  Your savings is someone else’s investment.  Nothing leaks out of the overall national system.  So as a household can increase income while cutting spending, a nation can not.  That would be like attempting to increase the amount of blood your heart pumps out while decreasing the amount of blood pumped in.  It won’t work.  And that is why Europe suffered a double dip recession in 2010 after governments scaled back spending in the aftermath of the 2008 financial crisis.  The effect of curtailing government spending during a recession amplifies the cycle.

It should be pointed out that resource utilization plays a role here.  The other counterargument to fiscal policy is that government spending is offset by spending reductions caused by taxes or buying of bonds.  If the economy is running at full capacity, that is correct.  If if is running at less than full capacity, and after a financial shock, it is well below full capacity, government spending puts underutilized resources to work.  The net effect is to increase GDP by more than what was spent by the government.  This multiplier effect has been empirically measured.

However, the key point here is if the household example is used to explain how a national economy behaves, the argument is improperly framed.  The same as true for the entropy/evolution debate.  Deciding what type of system you are working with is the foundation of your model.  If you build a square foundation for a round building, it will fail.  If you are going to attempt to predict an outcome and your model confuses an open system with a closed one or vise versa, you can expect pretty disappointing results.

*Image atop post credit: NASA.

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