Equilibrium - Biology As Poetry

Equilibrium is used as a default state for understanding how systems work, though in the case of bodies it is perturbation (existence) away from equilibrium which matters most

The goals of the associated laboratory exercise are to gain a sense of what equilibrium is by showing how probabilities, as rate constants, are all one needs to generate a reasonable approximation of a dynamic equilibrium or steady state.

At equilibrium things literally stay the same.

This can be a static equilibrium in which case things are staying the same because nothing is changing or it can be a dynamic equilibrium in which case things are staying the same because whatever forces that are acting are balancing each other. It is the latter that we are focusing on here.

It is important to remember in either case that equilibrium does not mean "equal" at any given time but instead "equal" over time. Thus, thing A need not equal thing B in terms of concentration but thing A's concentration today will equal thing A's concentration tomorrow (with the qualification of "more or less" because no matter what, we work with finite systems so statistical fluctuations happen).

Some examples of equilibria or steady states include: stable population sizes, water levels in ponds, an animal cell found in an isotonic medium, a plant cell found in a hypotonic medium.

We can think of equilibrium as what is achieved if we just let a system "fall" to its energy minimum. Alternatively, we can think of a steady state as the equivalent of an equilibrium except requiring an input of energy to maintain the balanced state.

Thus, in reality, populations remain stable in size because of ongoing births and births require energy (if we let a population truly go to equilibrium, then everybody would be dead). Thus, population stability in size technically is a steady state rather than an equilibrium even if we might "cheat" and say equilibrium instead.

Similarly, for a pond to remain constant in volume, something has to move the feeding water uphill and that takes energy as well, so in reality that too is a steady state, though again if we ignore that detail we might use the word equilibrium instead.

The example with cells, however, truly is an equilibrium, though even there, energy is required to keep the system going, in this case thermal energy. Indeed, energy is required to maintain any dynamic equilibrium, though that in and of itself does not mean that all dynamic equilibria are steady states.

The difference therefore between a dynamic equilibrium and a steady state is whether that energy is being employed specifically to maintain the observed balance, e.g., homeostasis in bodies, or instead whether the energy is happening in the background with the equilibrium representing just what the system "falls" to when no effort is being make to perturb the system literally away from equilibrium.

Keeping your house warm using a furnace therefore is unquestionably a steady state. If you turn off your furnace, however, your house will "fall" to whatever temperature represents a balance between natural heating such as from the ground and from the sun during the day minus loss of heat to the winter cold outside, and generally we would say that whatever temperature it achieves represents at that time a state of equilibrium.

Don't actively maintain (put energy into) anything and it will fall into a state of ~~disrepair~~ equilibrium, e.g., try not mowing a lawn!

To appreciate the concept of equilibrium it is helpful to begin with a teeter totter, i.e., a seesaw. Ignoring the up and down motion, instead consider just the balance between the two sides. That balance, when achieved with neither persons' feet on the ground, is an example of an equilibrium. Note that there are two aspects to this equilibrium, the weight of each individual involved and the distance between each of them and the balance point (there is also can be a third component to 'balancing acts', that of the expenditure of energy, which we'll get to a bit later).

On a teeter totter, if two individuals do not have the same weight (i.e., mass), then to balance, the heavier one needs to sit closer to the balance point (i.e., the fulcrum). This has to do with physics and lever arm lengths, but the important point for us is that the two sides don't have to be identical in all the same ways to be at equilibrium. Instead they can vary in more than one way, with those multiple ways adding up to generate an overall balance between the two sides.

In chemical equilibrium, the equivalent concepts are concentration (as the weight/mass equivalent) and rate constant, which is analogous to distance from the balance point (fulcrum). Thus at chemical equilibrium, rather than weight × lever arm length balancing, it instead is concentration × rate constant that balance. Another way of saying this is that if things take a long time to get going from place A to place B, then they will tend to build up in place A, and particularly so if those same things find it easy to get going from place B back to place A.

These ideas are also equivalent to the concept of handicapping in sports, where performance is evened out by some manner of penalizing the generally better performing individual or team. Make them carry weights while running, ride a bicycle with slower tires, or have to defend a larger goal, whatever. The important point is that you don't have to change both sides equivalently to create a balance between the two sides, that is, to establish an 'equilibrium'.

And so, what about energy? An equilibrium has the property of not requiring inputs of energy for its maintenance. Instead, an equilibrium can be viewed as an energy low, which also represents a stable configuration. Systems tend to move towards equilibrium because the inherent energy found within the system pushes them there, and in the course of this pushing, that energy is lost to the larger environment (i.e., as they say in physics, lost to the rest of the universe). The less energy that a system possesses, then the less it is able to do something, particularly all on its own. The less able something is to change, relying on whatever energy is available to it, then the more stable that something is. Particularly without inputs of additional energy, systems that are found at equilibrium consequently are stable systems.

Alternatively, it is also possible to have balances that do require an input of energy to maintain, and we call those balances steady states. If we return to the teeter-totter analogy, consider two sides that balance not because they have the same weight or have adjusted their positions relative to the fulcrum but instead because the heavier or more distant individual (or both!) balances their side by pushing against the ground with their feet. In this case what matters are masses, lever arm lengths, and the amount of force being applied to the ground. But since the latter requires an ongoing input of energy, the result is a steady state rather than strictly an equilibrium. For more on these latter ideas, see my essay, Equilibrium and Energy.