Instructor: Mark NewmanOffice: 322 West HallOffice hours: Tuesdays 1:30-3:30pmEmail: email@example.comGrader: Manavendra MahatoOffice: 3484F Randall LabOffice hours: Tuesdays 9:30-11:30amEmail: firstname.lastname@example.orgProblem session leader: Tom BabinecEmail: email@example.comProblem session time: Monday 7-9pmLocation: 337 West HallDescription: This course provides an introduction to thefundamentals of thermal physics including classical thermodynamics (thethree laws, temperature, internal energy, entropy, and applications) andstatistical mechanics (microscopic entropy, classical and quantum thermaldistributions, ideal gases, Fermi and Bose gases, thermal radiation,electrons in metals, Bose-Einstein condensation, superfluidity).
Austrian physicist Ludwig Boltzmann explained entropy as the measure of the number of possible microscopic arrangements or states of individual atoms and molecules of a system that comply with the macroscopic condition of the system. He thereby introduced the concept of statistical disorder and probability distributions into a new field of thermodynamics, called statistical mechanics, and found the link between the microscopic interactions, which fluctuate about an average configuration, to the macroscopically observable behavior, in form of a simple logarithmic law, with a proportionality constant, the Boltzmann constant, that has become one of the defining universal constants for the modern International System of Units (SI).
In 1948, Bell Labs scientist Claude Shannon developed similar statistical concepts of measuring microscopic uncertainty and multiplicity to the problem of random losses of information in telecommunication signals. Upon John von Neumann's suggestion, Shannon named this entity of missing information in analogous manner to its use in statistical mechanics as entropy, and gave birth to the field of information theory. This description has been identified as a universal definition of the concept of entropy.
For very small numbers of particles in the system, statistical thermodynamics must be used. The efficiency of devices such as photovoltaic cells requires an analysis from the standpoint of quantum mechanics.
The interpretation of entropy in statistical mechanics is the measure of uncertainty, disorder, or mixedupness in the phrase of Gibbs, which remains about a system after its observable macroscopic properties, such as temperature, pressure and volume, have been taken into account. For a given set of macroscopic variables, the entropy measures the degree to which the probability of the system is spread out over different possible microstates. In contrast to the macrostate, which characterizes plainly observable average quantities, a microstate specifies all molecular details about the system including the position and velocity of every molecule. The more such states are available to the system with appreciable probability, the greater the entropy. In statistical mechanics, entropy is a measure of the number of ways a system can be arranged, often taken to be a measure of "disorder" (the higher the entropy, the higher the disorder). This definition describes the entropy as being proportional to the natural logarithm of the number of possible microscopic configurations of the individual atoms and molecules of the system (microstates) that could cause the observed macroscopic state (macrostate) of the system. The constant of proportionality is the Boltzmann constant.
In what has been called the fundamental assumption of statistical thermodynamics or the fundamental postulate in statistical mechanics, among system microstates of the same energy (degenerate microstates) each microstate is assumed to be populated with equal probability; this assumption is usually justified for an isolated system in equilibrium. Then for an isolated system pi = 1/Ω, where Ω is the number of microstates whose energy equals the system's energy, and the previous equation reduces to
Furthermore, it has been shown that the definitions of entropy in statistical mechanics is the only entropy that is equivalent to the classical thermodynamics entropy under the following postulates:
I thought of calling it "information", but the word was overly used, so I decided to call it "uncertainty". [...] Von Neumann told me, "You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage."
Physically most accurate and computationally most expensive are non-empirical QM-based methods that describe the electronic structure and the atomic structures with all degrees of freedom. QM-based simulations are typically limited to small system sizes of less than thousand atoms and short time scales on the order of picoseconds. On the other end of the scale are simulation methods based on empirical molecular mechanics (MM) that do not explicitly describe the electronic structure and may additionally coarse-grain atomic structures by removing select degrees of freedom. Simulation methods that are direct non-empirical approximations to QM are (usually) transferable across the periodic table and across different atomic structures (e.g., organic molecules, bio-polymers, inorganic solids), whereas empirical methods are parametrized for a specific application and are typically not transferable to other situations. 2b1af7f3a8