# Overview: Thermodynamics and Statistical Physics

## Thermodynamics is the study of the energy associated with temperature

Thermodynamics (from the Greek words meaning "heat" and "power") is the study of the energy associated with temperature. It is what develops our understanding of what happens when objects heat up or cool down. From the physics point of view, it tells us that when resistive forces deplete the mechanical energy that we have defined as a part of our Newtonian framework, that the energy is not destroyed but transformed into another form — an energy internal to matter (thermal energy) by virtue of its temperature.

Thermodynamics shows us that even matter at normal temperatures contains huge amounts of thermal energy. This field of physics develops laws for the behavior of this energy and tells us under what circumstances the hidden thermal energy may be tapped to do useful work.

## Thermal energy is associated with the random motion of molecules

Our understanding of what this thermal energy actually is — kinetic and potential energies of the small particles of which matter is made — arises from studying how the macroscopic laws of thermodynamics arise from considering the motion of those particles. The critical difference between the motions we studied under the Newtonian framework and those we will study under the thermodynamic framework is this:

The energy associated with the motion of a macroscopic object studied using Newton's laws is coherent; that is, all parts of the object (or the segment of the object we are considering) move in the same way. The object has a net momentum associated with the kinetic energy we are considering.

The energy associated with the thermal energy of an object is incoherent; that is, the molecules of the object are moving in all directions randomly. Although the molecules have kinetic energy and momentum, the net momentum of the object as a result of its thermal energy is zero.

The study of how the macroscopic thermal behavior of objects arises from the motion of its molecules is called statistical mechanics.

## The biological implications

The flow and control of thermal energy are of considerable interest and importance to organisms, in part since the rates at which some of the critical chemical reactions of life take place depend on the temperature of the system. As a result, many organisms may spend a lot of the energy they harvest to regulate their temperatures. Understanding the thermal energy that is necessarily associated with chemical reaction chains such as photosynthesis, respiration, and the Krebs cycle is an important component of the energy balance of the reactions.

But perhaps even more important for modern biology is understanding the statistical mechanics of biological systems. The random motion of molecules plays a huge role in how the basic molecular mechanisms of biological systems take place, for example, the motion of uneven distributions of chemicals (chemical gradients, Fick's law, etc.), the self-assembly of viruses, and the replication of DNA. Our treatment of thermodynamics will therefore blend with a statistical mechanical description of the phenomena and an extended description of the role played by random molecular motions.

## Physics, chemistry, and biology

A word of warning: Thermodynamics (and occasionally some elements of statistical mechanics) is discussed in physics, chemistry, and biology classes. This might seem as if it would help, but in fact it often creates problems. The three fields each have their own "most important" aspects of these topics for their interests and they therefore may make different starting assumptions. Biologists often assume everything happens at constant pressures; chemists ignore coherent motions; physicists suppress chemical changes. While these may be perfectly reasonable assumptions for the examples they are each considering, often these assumptions are not highlighted. The choice of which thermodynamic variables to use and how to express the laws may be different. This means that the "laws of thermodynamics" may look different in your different classes! Here, we will do our best to include all forms of energy — at least as a basis for discussion — and to be explicit about what we choose to ignore in our various discussions

### Systems

Thermodynamics is about the forms energy can take and how it is transferred from one form to another. Since we presently believe that we know all the forms of energy that are relevant for biological processes* and we know that for the universe as a whole energy is conserved, the key thing is not that energy is conserved, but rather where does it go? This means that to study energy transformations we have to divide our universe into parts and look at how energy (and other thermodynamic variables such as entropy) are transferred between the parts. We have to divide the universe into the part we are paying attention to and the rest of the universe. The part we are paying attention to is called the system (of interest).

In some cases, we will be considering parts of a system that only exchange material and energy with each other. In this case, we refer to is as an isolated system. If energy can flow between the system but not matter, we refer to it as a  closed system. If the system we are looking at can exchange both matter and energy with the rest of the universe, we refer to it as an open system. While isolated systems are useful in order to get a sense of how energy flows, real biological systems typically have to be considered as open, as they exchange both energies and matter with their environments. This is less true when when considering large biological systems, such as ecosystems.  Ecosystems may be considered open or closed depending on whether you include the soil or oceans as part of the system. If you do, then they mostly exchange materials among themselves (food chains, soil, etc.), but the sun provides an outside source of energy that is critical to the functioning of the system.

In this section, we build an understanding of how energy can be distributed through the chemical, thermal, and mechanical levels and how the randomness inherent in thermal motion affects the natural and spontaneous distribution of energy.

• Heat and temperature — The basic concepts of thermodynamics, including heat, temperature, and pressure, can be developed macroscopically without an understanding of the underlying molecular theory. This section discusses those basic ideas.
• Kinetic theory — The dilute gas and the ideal gas law provides a natural place to develop a first understanding of how random thermal motion leads to macroscopic effects such as pressure and temperature.
• The 1st law of thermodynamics — The 1st law is the thermodynamic application of the principle of conservation of energy to thermal systems, relating internal (thermal) energy and macroscopic work. System thinking is critical here.
• The 2nd law of thermodynamics — The 2nd law a new kind of principle: a probabilistic physical law. Due to the large number of particles in the systems we typically consider, the randomness of thermal motion averages out and leads to a number of powerful tools, including:
• Entropy — This is a quantitative measure of how likely a particular distribution of energy is for a system. The 2nd law implies that the entropy of the universe (but NOT of subsystems) increases in all processes.
• Free energy — The 2nd law implies that energy can be extracted from the chemical and thermal energies present in a system and converted to useful work: but not all of it. Figuring out how much leads to the concept of free energy.
• Fluctuations — The 2nd law tells us that systems spontaneously move towards thermal equilibrium where energy is (in some sense) spread uniformly so that the average energy any place (the temperature) is the same. But this doesn't mean that it stays that way. It's only the average that remains the same: the energy is everywhere continually fluctuating and this has important implications for some biological processes.

* This is probably an excellent assumption. Molecular systems are so well studied that it is hard to imagine a new form of energy being discovered. On the other hand, the 2011 Nobel Prize in Physics was given for discovering that distant galaxies seem to be speeding up as they go away from us, not slowing down as the increases in their gravitational potential energy (it gets less negative as you get farther away) would predict. This suggests that either there is a new form of energy affecting the bigger-than-galactic scale or that on those (extremely large) distance scales, energy conservation no longer holds a supra-galactic scales. Stay tuned!

Julia Gouvea and Joe Redish 11/29/11

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