In the previous article, we looked at how thermodynamics began with the conservation of energy and led to the questions of entropy and the direction of nature. Now let us return to the question left at the end: “Why does nature move in the direction of increasing entropy?”
Boltzmann: Explaining entropy through the microscopic world
Clausius mathematically defined entropy and quantitatively described the direction of processes occurring in nature through the second law of thermodynamics. But he still could not explain why nature appears to move in the direction of increasing entropy. The person who brought a new perspective to this question was the Austrian physicist Ludwig Boltzmann. While Clausius described macroscopic phenomena in the language of thermodynamics, Boltzmann turned his attention to the atoms and molecules that give rise to those macroscopic laws. He tried to understand entropy through the microscopic movements of atoms and molecules.
At the time, not only had the existence of atoms not yet been experimentally demonstrated, but there were also many scientists who doubted their very existence and did not accept them as real physical objects. Nevertheless, Boltzmann believed that matter was made up of countless atoms and molecules, constantly moving and colliding. A single macroscopic state that we can see is actually the statistical result of the arrangements and motions of countless atoms and molecules. Think, for example, of a cup of water. We can simply describe it as water at about 25°C. But in reality, countless water molecules inside it are constantly moving, each at a different position and velocity. We cannot directly observe those individual movements. Instead, we perceive the average result produced by all those microscopic movements as a single state. Boltzmann called this average state that we can observe a macroscopic state, and distinguished the individual atomic arrangements and states of motion that produce it as microstates. His question was, “When there are so many microstates, why do some macroscopic states appear far more often than others?”
All molecules follow Newton’s laws of motion. In other words, molecules are not naturally stationary; they are always moving. As they move, they collide and change direction. The theory that describes this molecular motion is kinetic theory. For example, even if perfume is sprayed into one corner of a room, the perfume molecules constantly collide with air molecules and spread randomly in all directions, eventually appearing to fill the entire room. Yet we almost never observe perfume that has spread throughout the room gathering back into the corner where it was originally sprayed. Why? Not because this is physically impossible, but because the probability of it happening is almost zero. What Boltzmann wanted to explain was not why molecules move, but why, when enormous numbers of molecules come together, certain macroscopic directions appear far more often than others.
Kinetic theory: The movement of invisible atoms and molecules
In fact, even before the mid-19th century, many of the laws followed by gases were already well established experimentally. Scientists knew empirically that if pressure doubled, volume was halved; that volume increased as temperature rose; and that at the same temperature and pressure, equal volumes of gas contained equal numbers of particles. These relationships were later brought together in the ideal gas equation ($PV=nRT$). Here, an ideal gas is not a gas that actually exists, but the simplest gas model created for calculation. This equation describes the relationships among temperature, pressure, volume, and the amount of gas remarkably accurately, but no one could explain why such macroscopic laws appeared. James Clerk Maxwell then began to view a gas as a collection of countless molecules and used Newtonian mechanics to mathematically predict their velocities, representing them in a graph. He showed that not all molecules move at the same speed, but instead have different speeds that follow a particular probability distribution. On the graph, there are relatively few molecules at low and high speeds, while most are distributed around an intermediate speed. This is what we now call the Maxwell speed distribution. Maxwell went further, mathematically showing that pressure is related to the average effect of molecules colliding with the walls, while temperature is directly connected to the average kinetic energy of the molecules. He explained that in hot water, water molecules move faster on average, while in cold water they move more slowly on average. In other words, he mathematically connected macroscopic physical quantities such as temperature and pressure to the microscopic motion of molecules. This was where Boltzmann found great inspiration.
Boltzmann firmly believed that Newton’s laws of motion were the most fundamental laws, capable of accurately explaining all natural phenomena. He thought that heat, temperature, and entropy should also be explainable through Newtonian mechanics. But here a major contradiction appeared. Newton’s equation of motion ($F=ma$) has time reversibility: it remains valid even when time $t$ is replaced by $-t$. Yet, as we saw in the previous article, according to the second law of thermodynamics there is a clear direction of time in nature. Hot coffee cools but does not spontaneously become hot again, and heat flows from a higher temperature to a lower temperature but not in the opposite direction. If every atom follows Newton’s laws, why does macroscopic nature appear to move in only one direction? This was the problem Boltzmann wanted to solve.
Connecting kinetic theory and thermodynamics
If Maxwell predicted the motion of individual gas molecules and showed that their different speeds follow a particular statistical pattern, Boltzmann further generalised and systematised the statistical approach that Maxwell had begun. Instead of trying to track the motion of an almost unimaginable number of individual atoms, he began to develop a new way of looking at the whole statistically. At the time, introducing statistics into physics was a remarkably innovative approach. In a scientific world that viewed everything as already determined by laws, introducing the idea that “it may happen, or it may not” through statistics must have been an extraordinarily creative approach. It was also one of the places where his genius truly shone.
He thought that individual atoms still followed Newton’s laws, but if their number became enormous—tens or hundreds of trillions—we would observe not the motion of individual particles but the average behaviour produced by all of them together. In other words, the directionality of nature does not arise because individual atoms move in some special direction, but because of the probability distribution of the possible states that enormous numbers of atoms can produce. Here, the view of entropy changes completely. If, as Maxwell had shown, visible macroscopic physical quantities such as temperature and pressure are the result of the motions of countless invisible molecules, then entropy too might not simply be an abstract physical quantity, but a statistical result of microscopic states. For Boltzmann, entropy was no longer simply the mathematical state quantity defined by Clausius. It began to be understood in terms of the number of microstates that could produce a particular macroscopic state.
Let us take the example of tossing coins. When we toss coins, what we actually observe is a macrostate: “How many are heads, and how many are tails?” But a single macrostate can be made up of many different arrangements, or microstates. A macrostate in which heads and tails are mixed in similar numbers can be produced by a very large number of microstates. And because that number is overwhelmingly large, mixtures of heads and tails are observed most often. By contrast, if every coin comes up heads or every coin comes up tails, there is only one possible arrangement for each case, so these outcomes are observed far less often.
This becomes even clearer if we increase the number of coins. For example, when two coins are tossed, the probability that both come up heads is 1/4, and even with five coins, the probability that all come up heads is 1/32. If we repeat the experiment several times, this is something we could certainly observe. But what if we increase the number to just 100 coins? The probability that every one of them comes up heads becomes so small that we could practically say it would never happen. By contrast, a macrostate with roughly half heads and half tails can be produced by an enormous number of microstates. With 100 coins, there are about $2^{100} \approx 1.26765 \times 10^{30}$ possible microstates. This is an extraordinarily large number. Yet regardless of how many coins we toss, configurations in which heads and tails appear in roughly equal numbers overwhelmingly dominate and are the most probable. And as the number of particles increases, this probabilistic tendency goes beyond being merely a tendency and begins to look almost like an absolute law.
Gas molecules provide another good example. Even a fingernail-sized volume of air (1 cm³) contains about $2.7 \times 10^{19}$ molecules, while 1 mol of gas contains about $6.022 \times 10^{23}$ molecules. When such an unimaginably large number of particles are moving simultaneously, the number of possible microstates also becomes far beyond anything we can imagine. This is precisely why Boltzmann’s statistical explanation becomes much more powerful when describing systems containing enormous numbers of particles than when dealing with only a few atoms. So, as we saw earlier with the second law of thermodynamics, when nature appears to have a particular direction and to follow particular laws in various natural phenomena, this can in fact be understood as the statistical result produced by an enormous number of particles.
Time reversibility: Newton’s laws of motion still hold when time runs backwards
If we imagine distinguishing gas molecules one by one, there are effectively countless ways of producing a macrostate in which the molecules are spread throughout a box. If we could take photographs of the molecules at different moments while they were spread out, the molecules would show different positions and directions in every single frame. In other words, each frame would represent a possible microstate. By contrast, there are extremely few ways in which all the molecules could happen to be gathered into just one corner of the box. Without applying an external force, we would probably have to regard this as almost impossible. Yet if we consider Newton’s laws of motion alone, both states are physically possible. Nevertheless, what we almost always see is the gas spread throughout the box. This is not because nature specially chooses that state, but because the number of microstates capable of producing that macrostate is overwhelmingly large. What is possible and what is likely to happen frequently are entirely different matters. Nature does not produce all possible events with equal frequency. States that can be realised in overwhelmingly more ways appear statistically far more often. In other words, the gas does not spread simply because spreading is possible; we almost always observe it spread out because there are overwhelmingly more ways for it to be spread out. If the number of microstates producing a particular macrostate is overwhelmingly large, then macroscopically that state appears almost inevitable.
Newton’s laws of motion allow both a gas that has spread out to gather together again and a gas that is gathered together to spread out. This actually means that the same equations of motion remain valid even if time runs backwards.
In Newton’s equation of motion $F=ma$, acceleration is $a = \frac{d^2x}{dt^2}$ and velocity is $v = \frac{dx}{dt}$. Now suppose we reverse time so that $t \rightarrow -t$. Velocity then becomes $v = \frac{dx}{dt} \rightarrow -\frac{dx}{dt}$, so its direction is reversed. But acceleration is obtained by differentiating twice with respect to time, so the negative sign introduced by the first differentiation is multiplied by another negative sign in the second, giving $(-1)^2 = +1$. Therefore, $\frac{d^2x}{d(-t)^2} = \frac{d^2x}{dt^2}$, and acceleration does not change. Newton’s equation therefore remains equally valid whether time runs forwards or backwards.
And this conflicts with the second law of thermodynamics. Thermodynamics clearly tells us that hot coffee cools but does not spontaneously become hot again, and that perfume spreads through a room but does not spontaneously gather back into the bottle. In other words, nature appears to have a clear direction of time. Newton’s equations of motion, on the other hand, remain valid even when time is reversed and therefore predict that, in principle, both processes are possible. Boltzmann wanted to resolve precisely this problem. He explained that the direction of time is not contained within Newton’s laws themselves, but emerges from the statistical result produced by enormous numbers of particles. Movement in every direction, including the reverse direction, is theoretically possible, but we do not actually observe it because the number of microstates capable of producing such a state is overwhelmingly small. In other words, nature is not pulled towards increasing entropy by some special force. Rather, the direction in which there are overwhelmingly more possible ways for things to occur is the direction of increasing entropy, and so in the macroscopic world we almost always observe nature moving that way. From Boltzmann’s perspective, the second law of thermodynamics can be understood not so much as a new law competing with Newtonian mechanics, but as a macroscopic description of the statistical result produced by the microscopic motions of countless particles obeying Newton’s laws of motion. This is the essence of Boltzmann’s probabilistic view of nature.
Because there are overwhelmingly more microstates that can produce the macrostate in which molecules are spread throughout the box, in nature we almost always observe a state like the one on the left. From Boltzmann’s perspective, among the many directions that are microscopically possible, if one macroscopic phenomenon occurs statistically far more often than the others, we observe it as though it were a macroscopic law of nature.
Boltzmann’s definition of entropy
Boltzmann defined entropy as follows in order to mathematically express this “number of possible microstates”.
$$S = k \ln W$$
Here, $k$ is the Boltzmann constant, and $W$ is the total number of microstates that can produce a particular macrostate. But why do we use the natural logarithm and write $S = k \ln W$ instead of simply $S=W$? The reason is that entropy must be a physical quantity that adds when multiple systems are combined.
For example, suppose we have two independent systems, A and B. If the number of microstates available to box A is $W_1$ and the number available to box B is $W_2$, then when the two boxes are combined into one larger system, the total number of possible microstates, $W_{\mathrm{total}}$, is as follows: $W_{\mathrm{total}} = W_1 W_2$. This is because for every microstate of box A, box B can in turn have $W_2$ different states. It is similar to putting together an outfit. If you have five tops and four pairs of trousers, there are $5 \times 4 = 20$ possible outfit combinations. The numbers of independent possibilities are multiplied together.
Entropy, however, has the property that when two systems are combined, their entropies add: $S_{\mathrm{total}} = S_1 + S_2$. In physics, a quantity with this property is called extensive. The properties of logarithms allow both conditions to be satisfied at the same time, because $\ln(ab) = \ln a + \ln b$. Therefore, if we define entropy as $S = k \ln W$,
$$S_{\mathrm{total}} = k \ln (W_1 W_2)$$
$$S_{\mathrm{total}} = k \ln W_1 + k \ln W_2$$
$$S_{\mathrm{total}} = S_1 + S_2$$
so the numbers of microstates multiply while the entropies add. In other words, the logarithm was not added merely to make the calculation convenient. It is a necessary function for satisfying the additive physical property of entropy.
Boltzmann’s equation becomes particularly powerful as the number of particles making up a system becomes very large. As the number of particles increases, the number of possible microstates $W$ becomes unimaginably large, and the difference in the numbers of microstates between different macrostates also grows exponentially. As a result, a macrostate with overwhelmingly many microstates is observed almost all the time, while one with extremely few microstates is, in practice, almost never observed even though it is physically possible. We may feel that nature chooses a particular direction, but in reality there is no force or law selecting that particular direction. We almost always observe it simply because there are overwhelmingly more microstates capable of producing it. This is why the directionality of nature appears to us like a law.
In a real gas containing about $10^{23}$ molecules, this statistical bias becomes effectively absolute. Statistical mechanics therefore becomes more powerful as the number of particles increases and provides a key explanation for why macroscopic natural phenomena have a particular direction. Boltzmann explained that nature is not “pulled” towards increasing entropy; rather, that direction is statistically observed because there are overwhelmingly more microstates that realise it.
Entropy is not ‘disorder’
There is one point here that I particularly want to address. If you search for entropy now, probably the explanation or related search term you will encounter most often is ‘disorder’. Personally, I wonder whether avoiding the word disorder as much as possible might actually help us understand entropy better. It is also difficult to deny that the word disorder already carries a slightly negative value judgement. Many scientists explain entropy using a photograph of a messy room, describing it as disordered and therefore high in entropy. What matters is not the fact that the room is messy, but the fact that there are overwhelmingly many ways of producing that state. Entropy is not a quantity that measures disorder itself, but a physical quantity representing the number of possible microstates that can produce a particular macrostate. A messy state is not the direction that nature has chosen. There are simply many ways for things to become messy, and it is in that sense that we say the entropy is high. Disorder and randomness are related to entropy, but let us not confuse them with entropy itself.
We have now understood Boltzmann’s definition of entropy. Let us go a little further and explore free energy. By connecting entropy to the number of microstates, Boltzmann succeeded in explaining the physical meaning of the second law of thermodynamics. But this alone is still not enough to understand life. Living organisms do not simply move in the direction of increasing entropy. Energy and entropy always act together, and the concept that considers both at the same time is free energy. By understanding what free energy is, I hope we can see how this leads to a theory that explains protein folding.
An old question for chemists: “Why do substances attract one another and react?”
Through the work of Clausius and Boltzmann, it became clear that the spontaneous changes selected by nature—the direction of natural phenomena in which cooled coffee does not spontaneously become hot again and a stone rolls only downhill—are directly connected to increasing entropy. The macroscopic phenomena we observe in nature do not occur because nature possesses some special force or intention. Rather, the number of microstates ($W$) that can statistically produce such macroscopic forms is overwhelmingly large, so to our eyes we almost always observe only that one direction.
In chemistry, such phenomena that occur on their own without external intervention are called spontaneous processes. In fact, even before the concept of entropy was established, chemists had long faced the problem of explaining why, when two substances met, some reactions occurred explosively while others did not occur at all. At the time, when chemists saw a reaction readily producing products, they would vaguely explain that the two reactants had a strong affinity for each other. But they could not explain the fundamental reason why some substances had affinity for one another while others did not react. Discovering the true nature of spontaneity in nature and chemical affinity was probably one of the major scientific questions of the time.
Predicting a reaction without measuring the entropy of the entire universe
Of course, using Boltzmann’s definition of entropy ($S = k \ln W$), we could in theory determine whether a reaction will occur spontaneously by calculating the number of microstates ($W$) available to the molecules after the reaction. If the total number of possible microstates after the reaction ($W_{\text{after}}$) is greater than before the reaction ($W_{\text{before}}$), so that entropy increases ($\Delta S > 0$), then this is the direction of the spontaneous process selected by nature. But was this realistically possible for scientists studying chemical reactions in a laboratory? Even a few grams of reagent in a beaker may contain about 1 mol, or more than $10^{23}$ molecules. Counting all the combinations of microstates ($W$) produced by the positions and energies of every one of these molecules would be almost impossible. Nor would it make sense, following Clausius’s approach, to measure directly the entropy changes of both the beaker (the system) and all the surrounding laboratory air (the surroundings) every time a reaction took place. $\Delta S_{\text{total}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} \ge 0$
It was in this situation that the American physicist Josiah Willard Gibbs found a way to predict whether a reaction would occur spontaneously using only information from inside the beaker—the system. Gibbs found an important connection: the heat exchanged between the system and its surroundings is related to the system’s enthalpy change. Using this relationship, the direction of the total entropy change could be determined from the enthalpy and entropy changes of the system without directly calculating the entropy change of the surroundings ($\Delta S_{\text{surroundings}}$). Let us briefly look at how he derived the equation.
First, the entropy change of the entire universe is equal to the entropy change of the system we are interested in plus that of the surroundings.
$$\Delta S_{\text{total}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} \ge 0$$
We need to express the entropy change of the surroundings ($\Delta S_{\text{surr}}$) in terms of variables of the system that we can measure more easily. According to the law of conservation of energy, or the first law of thermodynamics, heat released by the system is absorbed by the surroundings, while heat absorbed by the system is lost by the surroundings. Therefore, the two are related as follows.
$$q_{\text{surr}} = -q_{\text{sys}}$$
Now recall the enthalpy discussed earlier with the first law of thermodynamics. We have already looked in detail at how, if a chemical reaction takes place at constant pressure and the only work done by the system is $PV$ work, the amount of heat absorbed or released during the reaction can be represented by the enthalpy change $\Delta H$. Since most chemical reactions take place at constant pressure, such as atmospheric pressure, we can write
$$q_{\text{sys}} = \Delta H_{\text{sys}}$$
And the entropy change of the surroundings is equal to the heat gained by the surroundings divided by the absolute temperature. $\Delta S = \frac{q_{\text{rev}}}{T}$
Therefore, the entropy change of the surroundings can be written as
$$\Delta S_{\text{surr}} = \frac{q_{\text{surr}}}{T} = -\frac{\Delta H_{\text{sys}}}{T}$$
Now substitute this expression for $\Delta S_{\text{surr}}$ into the entropy equation for the universe.
$$\Delta S_{\text{univ}} = \Delta S - \frac{\Delta H}{T}$$
Written in this form, we no longer need to observe the surroundings directly. We can determine the entropy change of the entire universe using only the temperature ($T$), enthalpy ($\Delta H$), and entropy ($\Delta S$) of the system. From this point onwards, unless otherwise indicated, $\Delta H$ and $\Delta S$ refer to values for the system. To rearrange the equation further, let us multiply both sides by $-T$.
$$-T\Delta S_{\text{univ}} = \Delta H - T\Delta S$$
Here, the quantity $-T\Delta S_{\text{univ}}$ can be represented by a state function called the system’s Gibbs free energy change ($\Delta G$).
$$\Delta G \equiv -T\Delta S_{\text{univ}}$$
This gives the familiar free energy equation.
$$\Delta G = \Delta H - T\Delta S$$
At constant temperature and pressure, we can therefore use the system’s $\Delta G$ to determine, from information about the system alone, whether the total entropy of the system and surroundings increases. A new physical quantity had been found that allowed the spontaneity of a reaction to be judged using only information about the system, without measuring the entropy of the entire universe. But in fact, much more important than how this equation is derived mathematically is how we interpret and use it.
Free energy? Does it mean energy for free?
There is one point to clarify here. Because of the name free energy, it is easy to imagine some special form of physical energy that is stored somewhere or actually exists, but free energy is not stored energy like heat or kinetic energy. Free energy is a state function that describes the state of a system, and it is a physical quantity used as an indicator for predicting and judging how stable the system is under given conditions and whether it has the potential to do useful work on its surroundings. And the word Free here is closer to the free in the question, “Are you free today?” In other words, free does not mean without cost. It is closer to the idea of how much capacity remains, under given conditions, to be converted into other forms of work. Because of this misunderstanding, there have apparently long been calls to drop the word Free and simply call it ‘Gibbs energy’.
Gibbs free energy: What does it tell us?
Gibbs transformed the enormous thermodynamic condition of increasing entropy in the entire universe into a practical criterion that, at constant temperature and pressure, can be judged using only the change in the system’s free energy, $\Delta G$. What can this equation tell us?
$\Delta G < 0$ (negative): At constant temperature and pressure, change occurs spontaneously in that direction.
$\Delta G > 0$ (positive): It does not proceed spontaneously in that direction, and energy must be supplied from outside.
$\Delta G = 0$: At constant temperature and pressure, this corresponds to equilibrium, where the forward and reverse changes are balanced.
The spontaneity of nature, which chemists in the past had described using the vague language of ‘affinity’, could now be brought into the realm of science, where the direction of a reaction could be measured and predicted on the clear basis of Gibbs free energy. One point to keep in mind is that spontaneity does not tell us how quickly a reaction occurs. Thermodynamics can tell us in which direction a change can proceed, but whether that change occurs quickly or slowly is determined by kinetics.
Gibbs free energy: Nature’s decision-making function
$$\Delta G \equiv -T\Delta S_{\text{univ}}$$
From this definition, because the absolute temperature $T$ is always positive, we can see an important relationship: at constant temperature and pressure, a process in which the entropy of the universe increases corresponds exactly to a process in which the free energy of the system decreases. The second law of thermodynamics described the direction of nature as the direction of increasing entropy, and Gibbs expressed the same idea differently, as the direction of decreasing free energy of the system under conditions of constant temperature and pressure. Gibbs transformed the enormous thermodynamic condition of increasing entropy in the entire universe into a practical criterion that could be judged from the system’s free energy change $\Delta G$ at constant temperature and pressure. In this sense, we might compare Gibbs free energy to nature’s decision-making function, allowing us to judge which direction among countless possible states is thermodynamically more favourable.
Then which does nature consider more important, enthalpy or entropy? In reality, it does not choose one over the other. Nature takes both effects into account at the same time, and the physical quantity that represents their combined result is Gibbs free energy. To see why free energy becomes a criterion for judging which state nature will choose, consider water and oil. Why do water and oil not mix? When the two are mixed, the number of possible microstates becomes more diverse, producing an entropy-increasing effect. But there is also a large energetic cost associated with the molecular interactions between water and oil and with rearranging water’s hydrogen-bonding network. Therefore, if the combined effect of these two factors causes free energy to increase, the mixed state is unstable and the two spontaneously separate again.
Free energy and protein folding
Now, as we bring these two long articles to a close, let us return to our starting point. Why does nature arrive at a particular state among countless possible states? Clausius described the direction of nature in the macroscopic world in terms of increasing entropy, and Boltzmann went one step further by connecting that entropy to the number of possible microstates. Gibbs then translated this enormous statistical law into the language of free energy, which could actually be used in chemistry and physics. The ultimate reason Gibbs developed free energy was not simply to calculate energy, but to predict which state nature would select from among countless possibilities. Just as improving thermal efficiency was a major concern for scientists against the background of the Industrial Revolution in the early 19th century, modern scientists have sought to understand how proteins, macromolecules essential for sustaining life, fold. They have asked a practical question: among the countless possible structures a protein can adopt, why does nature select that particular native structure?
$$\Delta G = \Delta H - T\Delta S$$
Gibbs’s free energy equation contains two competing factors. One is enthalpy, which represents the energetic stability of the system, and the other is entropy, which is connected to the number of possible microstates. A spontaneous change in nature does not simply follow one of these two factors alone. Its direction is determined by the change in free energy produced by the two effects together under the given conditions. And this perspective applies equally to living systems.
In protein folding, entropy and enthalpy compete with each other. A newly formed, unfolded polypeptide chain has many conformational degrees of freedom, so the conformational entropy of the protein chain itself is relatively high. As the protein gradually folds towards a particular structure, these degrees of freedom decrease, causing the entropy of the chain to decrease. But we cannot look only at the protein. We must also consider the surrounding aqueous environment. In particular, when hydrophobic residues are in contact with water, the surrounding water molecules must adopt particular arrangements around the hydrophobic surfaces. As the protein folds and hydrophobic residues move away from water and become buried together inside the protein structure, this constraint on the arrangement of the water molecules is greatly reduced, increasing the entropy of the water solvent. At the same time, van der Waals interactions, hydrogen bonds, electrostatic interactions, and other interactions within the protein contribute to the enthalpy change.
A protein can adopt countless possible structures, but not all of them are equally stable. Many factors—including the protein’s own conformational freedom, interactions with water, the hydrophobic effect, hydrogen bonds, and van der Waals interactions—compete with one another to create a particular free-energy landscape. The protein undergoes thermal fluctuations on this landscape and moves between different states, eventually remaining in stable regions formed by thermodynamically favourable states. This is the perspective described by protein energy landscape theory. Gibbs free energy is used to predict the direction in which nature selects a state from among countless possibilities.
Protein folding is neither simply a process in which energy decreases nor simply one in which entropy increases. It proceeds in the direction of decreasing free energy for the entire system, including the protein and the surrounding solvent. The modern theory that describes how a protein moves across this free-energy landscape is energy landscape theory.
In fact, I began studying thermodynamics again in order to properly understand energy landscape theory, a theory of protein folding. It was a meaningful opportunity to understand that natural phenomena ranging from hot coffee cooling down to the biological phenomenon of protein folding can all be explained through the same thermodynamic principles.
[Image sources]
Image 1-1. Coin Tosses and Probability — CC BY 4.0. Created with reference to this sourceImage 2-1. Figure 114.2 — CC BY 4.0.
