Relationship between physics and statistics

Statistical Physics - Definition, Mechanics, Thermodynamics & Examples | [email protected]

relationship between physics and statistics

Physics is a method of studying nature, usually at its most fundamental level. What is the difference between statistical mechanics and statistical physics? What is the relationship between mathematical physics and theoretical physics?. as well as in the physics literature, the terminology of the “ZP state” and the “ZP .. [23] deduces the relationship between this radiation pressure and the energy . Statistical physics is a branch of physics that uses methods of probability theory and statistics, Historically, one of the first topics in physics where statistical methods were applied was the field of mechanics, which is concerned with the motion.

For instance, when we exert a force on a volume of gas in the form of a pressure, the gas will contract. When we give energy in the form of a pressure, the gas either expand or increase its pressure.

There are general relationships between these responses. Thermodynamics gives us such relationships. This branch of physics evolved from the necessity to increase the efficiency of the conversion of heat to work, which became important after the industrial revolution.

The laws of thermodynamics are quite general; they are independent of the species of the atoms from which the matter is constructed and independent of the interactions between the atoms. Statistical mechanics as Balescu states is the "mechanics of large assemblies of simple systems such as molecules in a gas, atoms in a crystal".

In chemistry we are interested in the prediction of macroscopic bulk properties such as pressure and density which are obviously related to the properties of individual atoms and molecules. The purpose of statistical mechanics is "to understand the behavior of the assembly as a whole in terms of the behavior of its constituents" using statistical considerations. This basic tenet provides the foundation for the subject of statistical thermodynamics. It is denoted by the symbol kB.

A student being introduced to physics first encounters the fundamental theories, for instance Newtonian mechanics, electrodynamics and the theory of relativity, and see in these the ideals of a scientific theory. In statistical mechanics it seems that statistics has to be taken serious. However, when one inspects theories on statistical mechanics to see how they present the concepts of probability theory.

A physicist who is confronted with the interpretation of experimental results for a thesis, or who wishes to analyze the effects of complex systems in his or her later profession, will almost inevitably find that this cannot be done without the application of statistical methods. Limited information about the dynamics of a system and uncontrollable influences on the system often mean that is can only be considered as a statistical system. And apart from that, when analyzing experimental data, one always has to take into account that any measured value has an uncertainty expressed by its error.

One should not only expect limited knowledge but one should also know how to deal with it. This early chemistry was very important for physics. The interaction between the two sciences was very great because the theory of atoms was substantiated to a large extent by experiments in chemistry. The theory of chemistry, i. All these rules were ultimately explained in principle by quantum mechanics, so that theoretical chemistry is in fact physics.

On the other hand, it must be emphasized that this explanation is in principle. We have already discussed the difference between knowing the rules of the game of chess, and being able to play.

So it is that we may know the rules, but we cannot play very well. It turns out to be very difficult to predict precisely what will happen in a given chemical reaction; nevertheless, the deepest part of theoretical chemistry must end up in quantum mechanics. There is also a branch of physics and chemistry which was developed by both sciences together, and which is extremely important. This is the method of statistics applied in a situation in which there are mechanical laws, which is aptly called statistical mechanics.

In any chemical situation a large number of atoms are involved, and we have seen that the atoms are all jiggling around in a very random and complicated way.

  • Statistical Physics

If we could analyze each collision, and be able to follow in detail the motion of each molecule, we might hope to figure out what would happen, but the many numbers needed to keep track of all these molecules exceeds so enormously the capacity of any computer, and certainly the capacity of the mind, that it was important to develop a method for dealing with such complicated situations.

Statistical mechanics, then, is the science of the phenomena of heat, or thermodynamics. Inorganic chemistry is, as a science, now reduced essentially to what are called physical chemistry and quantum chemistry; physical chemistry to study the rates at which reactions occur and what is happening in detail How do the molecules hit? Which pieces fly off first?

Mod-01 Lec-25 Connection between statistical mechanics and ther-modynamics

The other branch of chemistry is organic chemistry, the chemistry of the substances which are associated with living things. For a time it was believed that the substances which are associated with living things were so marvelous that they could not be made by hand, from inorganic materials.

This is not at all true—they are just the same as the substances made in inorganic chemistry, but more complicated arrangements of atoms are involved. Organic chemistry obviously has a very close relationship to the biology which supplies its substances, and to industry, and furthermore, much physical chemistry and quantum mechanics can be applied to organic as well as to inorganic compounds. However, the main problems of organic chemistry are not in these aspects, but rather in the analysis and synthesis of the substances which are formed in biological systems, in living things.

This leads imperceptibly, in steps, toward biochemistry, and then into biology itself, or molecular biology. In the early days of biology, the biologists had to deal with the purely descriptive problem of finding out what living things there were, and so they just had to count such things as the hairs of the limbs of fleas. After these matters were worked out with a great deal of interest, the biologists went into the machinery inside the living bodies, first from a gross standpoint, naturally, because it takes some effort to get into the finer details.

There was an interesting early relationship between physics and biology in which biology helped physics in the discovery of the conservation of energy, which was first demonstrated by Mayer in connection with the amount of heat taken in and given out by a living creature.

If we look at the processes of biology of living animals more closely, we see many physical phenomena: It is interesting how that happens. In their study of nerves, the biologists have come to the conclusion that nerves are very fine tubes with a complex wall which is very thin; through this wall the cell pumps ions, so that there are positive ions on the outside and negative ions on the inside, like a capacitor. This in turn affects it farther along, etc.

This wave is somewhat analogous to a long sequence of vertical dominoes; if the end one is pushed over, that one pushes the next, etc. Of course this will transmit only one message unless the dominoes are set up again; and similarly in the nerve cell, there are processes which pump the ions slowly out again, to get the nerve ready for the next impulse.

So it is that we know what we are doing or at least where we are. Of course the electrical effects associated with this nerve impulse can be picked up with electrical instruments, and because there are electrical effects, obviously the physics of electrical effects has had a great deal of influence on understanding the phenomenon.

The opposite effect is that, from somewhere in the brain, a message is sent out along a nerve. What happens at the end of the nerve? There the nerve branches out into fine little things, connected to a structure near a muscle, called an endplate. For reasons which are not exactly understood, when the impulse reaches the end of the nerve, little packets of a chemical called acetylcholine are shot off five or ten molecules at a time and they affect the muscle fiber and make it contract—how simple!

What makes a muscle contract? A muscle is a very large number of fibers close together, containing two different substances, myosin and actomyosin, but the machinery by which the chemical reaction induced by acetylcholine can modify the dimensions of the muscle is not yet known. Thus the fundamental processes in the muscle that make mechanical motions are not known.

The Feynman Lectures on Physics Vol. I Ch. 3: The Relation of Physics to Other Sciences

Biology is such an enormously wide field that there are hosts of other problems that we cannot mention at all—problems on how vision works what the light does in the eyehow hearing works, etc. The way in which thinking works we shall discuss later under psychology.

Now, these things concerning biology which we have just discussed are, from a biological standpoint, really not fundamental, at the bottom of life, in the sense that even if we understood them we still would not understand life itself. But you can have life without nerves. Plants have neither nerves nor muscles, but they are working, they are alive, just the same. So for the fundamental problems of biology we must look deeper; when we do, we discover that all living things have a great many characteristics in common.

The most common feature is that they are made of cells, within each of which is complex machinery for doing things chemically. In plant cells, for example, there is machinery for picking up light and generating glucose, which is consumed in the dark to keep the plant alive.

When the plant is eaten the glucose itself generates in the animal a series of chemical reactions very closely related to photosynthesis and its opposite effect in the dark in plants. In the cells of living systems there are many elaborate chemical reactions, in which one compound is changed into another and another.

To give some impression of the enormous efforts that have gone into the study of biochemistry, the chart in Fig. Here we see a whole series of molecules which change from one to another in a sequence or cycle of rather small steps. It is called the Krebs cycle, the respiratory cycle. Each of the chemicals and each of the steps is fairly simple, in terms of what change is made in the molecule, but—and this is a centrally important discovery in biochemistry—these changes are relatively difficult to accomplish in a laboratory.

If we wanted to take an object from one place to another, at the same level but on the other side of a hill, we could push it over the top, but to do so requires the addition of some energy. Thus most chemical reactions do not occur, because there is what is called an activation energy in the way. In order to add an extra atom to our chemical requires that we get it close enough that some rearrangement can occur; then it will stick.

relationship between physics and statistics

However, if we could literally take the molecules in our hands and push and pull the atoms around in such a way as to open a hole to let the new atom in, and then let it snap back, we would have found another way, around the hill, which would not require extra energy, and the reaction would go easily.

Now there actually are, in the cells, very large molecules, much larger than the ones whose changes we have been describing, which in some complicated way hold the smaller molecules just right, so that the reaction can occur easily. These very large and complicated things are called enzymes.

They were first called ferments, because they were originally discovered in the fermentation of sugar. In fact, some of the first reactions in the cycle were discovered there. In the presence of an enzyme the reaction will go.

An enzyme is made of another substance called protein. Enzymes are very big and complicated, and each one is different, each being built to control a certain special reaction. The names of the enzymes are written in Fig. Sometimes the same enzyme may control two reactions. We emphasize that the enzymes themselves are not involved in the reaction directly. They do not change; they merely let an atom go from one place to another.

Having done so, the enzyme is ready to do it to the next molecule, like a machine in a factory. Of course, there must be a supply of certain atoms and a way of disposing of other atoms. Take hydrogen, for example: For example, there are three or four hydrogen-reducing enzymes which are used all over our cycle in different places. It is interesting that the machinery which liberates some hydrogen at one place will take that hydrogen and use it somewhere else.

The most important feature of the cycle of Fig. So, GTP has more energy than GDP and if the cycle is going one way, we are producing molecules which have extra energy and which can go drive some other cycle which requires energy, for example the contraction of muscle.

relationship between physics and statistics

The muscle will not contract unless there is GTP. An enzyme, you see, does not care in which direction the reaction goes, for if it did it would violate one of the laws of physics. Physics is of great importance in biology and other sciences for still another reason, that has to do with experimental techniques.

In fact, if it were not for the great development of experimental physics, these biochemistry charts would not be known today. The reason is that the most useful tool of all for analyzing this fantastically complex system is to label the atoms which are used in the reactions. They are different isotopes. We recall that the chemical properties of atoms are determined by the number of electrons, not by the mass of the nucleus.

But there can be, for example in carbon, six neutrons or seven neutrons, together with the six protons which all carbon nuclei have.

Statistical physics

Now, we return to the description of enzymes and proteins. Not all proteins are enzymes, but all enzymes are proteins. There are many proteins, such as the proteins in muscle, the structural proteins which are, for example, in cartilage and hair, skin, etc. However, proteins are a very characteristic substance of life: Proteins have a very interesting and simple structure. They are a series, or chain, of different amino acids.

The Relationships Between Statistics and Other Subjects in the K–12 Curriculum | CHANCE

There are twenty different amino acids, and they all can combine with each other to form chains in which the backbone is CO-NH, etc.

Proteins are nothing but chains of various ones of these twenty amino acids. Each of the amino acids probably serves some special purpose. Some, for example, have a sulfur atom at a certain place; when two sulfur atoms are in the same protein, they form a bond, that is, they tie the chain together at two points and form a loop.

Another has extra oxygen atoms which make it an acidic substance, another has a basic characteristic. Some of them have big groups hanging out to one side, so that they take up a lot of space. One of the amino acids, called proline, is not really an amino acid, but imino acid.

There is a slight difference, with the result that when proline is in the chain, there is a kink in the chain. If we wished to manufacture a particular protein, we would give these instructions: In this way, we will get a complicated-looking chain, hooked together and having some complex structure; this is presumably just the manner in which all the various enzymes are made. One of the great triumphs in recent times sincewas at last to discover the exact spatial atomic arrangement of certain proteins, which involve some fifty-six or sixty amino acids in a row.

Over a thousand atoms more nearly two thousand, if we count the hydrogen atoms have been located in a complex pattern in two proteins. The first was hemoglobin. One of the sad aspects of this discovery is that we cannot see anything from the pattern; we do not understand why it works the way it does.

Of course, that is the next problem to be attacked. Another problem is how do the enzymes know what to be? A red-eyed fly makes a red-eyed fly baby, and so the information for the whole pattern of enzymes to make red pigment must be passed from one fly to the next.

This is done by a substance in the nucleus of the cell, not a protein, called DNA short for desoxyribose nucleic acid. This is the key substance which is passed from one cell to another for instance sperm cells consist mostly of DNA and carries the information as to how to make the enzymes. First, the blueprint must be able to reproduce itself. Secondly, it must be able to instruct the protein. Concerning the reproduction, we might think that this proceeds like cell reproduction.

Cells simply grow bigger and then divide in half. Must it be thus with DNA molecules, then, that they too grow bigger and divide in half? Every atom certainly does not grow bigger and divide in half!

No, it is impossible to reproduce a molecule except by some more clever way. Schematic diagram of DNA. The structure of the substance DNA was studied for a long time, first chemically to find the composition, and then with x-rays to find the pattern in space. The result was the following remarkable discovery: The DNA molecule is a pair of chains, twisted upon each other. The backbone of each of these chains, which are analogous to the chains of proteins but chemically quite different, is a series of sugar and phosphate groups, as shown in Fig.

Thus perhaps, in some way, the specific instructions for the manufacture of proteins are contained in the specific series of the DNA. Attached to each sugar along the line, and linking the two chains together, are certain pairs of cross-links. Whatever the letters may be in one chain, each one must have its specific complementary letter on the other chain. What then about reproduction? Suppose we split this chain in two. How can we make another one just like it? This is the central unsolved problem in biology today.

The first clues, or pieces of information, however, are these: There are in the cell tiny particles called ribosomes, and it is now known that that is the place where proteins are made. But the ribosomes are not in the nucleus, where the DNA and its instructions are. Something seems to be the matter. However, it is also known that little molecule pieces come off the DNA—not as long as the big DNA molecule that carries all the information itself, but like a small section of it.

This is called RNA, but that is not essential. It is a kind of copy of the DNA, a short copy. The RNA, which somehow carries a message as to what kind of protein to make goes over to the ribosome; that is known. When it gets there, protein is synthesized at the ribosome. That is also known.

However, the details of how the amino acids come in and are arranged in accordance with a code that is on the RNA are, as yet, still unknown.

We do not know how to read it. Certainly no subject or field is making more progress on so many fronts at the present moment, than biology, and if we were to name the most powerful assumption of all, which leads one on and on in an attempt to understand life, it is that all things are made of atoms, and that everything that living things do can be understood in terms of the jigglings and wigglings of atoms.