Entropy of an ideal gas: A similar relation holds for any exchanged quantity. Lecture 9 Pg 11 Summary • The total entropy of an isolated system is maximum in equilibrium. Degeneracy: an energy level contains more than one energy state. • So if two parts (1 and 2) can exchange V, equilibrium requires: This is a general equilibrium condition. As an analogy, consider a national presidential election. A microstate is a specific arrangement of the constituent parts of a system that produces an externally observable macrostate. 2. A single macrostate contains a very large number of microstates. ( , ) ↑ ↓ ↑ ↑ ↑ − Ω = = N N N N N N N N N For a two-state paramagnet in zero field, the energy of all macrostates is the same (0). Thermodynamic probability: the number of microstates leading to a given macrostate. ≡1 (exactly one way to arrange zero objects)! Therefore, one macrostate may contain several different microstates. The microstate is specified by the quantum state of each particle in a system (for an Einstein solid # of the quanta of energy for each of N oscillators) 3. ( )!!! !! For example, the changes in the microstate can be as small as 10 35 times than a macrostate, but there are still changes in this scale which may have no effect at the macrostate. The macrostate is specified by a sufficient number of macroscopically measurable parameters (for an Einstein solid N and U). In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations. For example, consider a box containing two particles and only one quantized unit of energy (meaning it can't be divided up; it must go entirely to one of the two particles). In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature, pressure, volume and density. The macrostates are the various possible winners of the election, and the microstates are the various combinations of ways in which the voters may cast their ballots. Its multiplicity - the number of ways of choosing N↑ objects out of N : N Ω = ( ,0) 1 ( ,1) Ω = N N Microstate: is specified by the number of particles in each energy state. For Treatments on statistical mechanics define a macrostate as follows: a … A macrostate is an overview of a complex situation, whereas a microstate describes the details of how each element of the system functions. The multiplicity is the number of microstates in a macrostate. It is donated by Wk where k represents the kth macrostate. A macrostate is specified by (N, N↑). n 0 ! In contrast to the macrostate, which characterizes plainly observable average quantities (temperature, for example), a microstate specifies all molecular details about the system, including the position and velocity of every molecule. With more available microstates, the entropy of a system increases.

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