Chapter 5. Thermodynamic processes:
Although thermodynamics strictly speaking refers only to equilibria, by introducing
the concept of work flow and heat flow, as discussed in chapter 1, we can discuss
processes by which a system is moved from one state t
Chapter 8. Phase transitions
When chemical reactions occur, the system makes transition among multiple minima at
the molecular level. The figure below illustrates the molecular connection between free
energy G, its derivative G, and the free energy as a f
Chapter 6. The solution of thermodynamic problems:
With U, A, H and G in hand we have potentials as a functions of whichever variable pair
we want: S and V, to T and P. Additional Legendre transforms will provide us with
further potentials in case we have
4. More general extremum principles and thermodynamic potentials
We have seen that mincfw_U(S, X ) and maxcfw_S(U, X) imply one another. Under
certain conditions, these principles are very convenient. For example,
dS =
1
P
dU dV + i dn i max i dn i
T
Chapter 2 The Postulates of Thermodynamics
Thermodynamics has three important ingredients: fundamental relations, which describe
the relationship between state functions for a particular system; postulates that make
statements about the state functions fr
Chapter 11. The microcanonical ensemble
The goal of equilibrium statistical mechanics is to calculate the diagonal elements of eq
= A that give us fundamental
eq
so we can evaluate average observables < A >= Trcfw_ A
relations or equations of state.
Ju
Chapter 3 - Basic properties of U, S, and their differentials
S
1. Energy minimum principle
S can be written as S(U, X ) , where X is a
vector of all independent internal extensive
variable (e.g. all but one Uk, and all other Xi).
Because S is monotonic i
Chapter 12. The canonical ensemble
To discuss systems at constant T, we need to embed them with a diathermal wall in a heat
bath. Note that only the system and bath need to be large for Wtot and Wbath to satisfy the
large number approximations, W Wsys can
Chapter 7 - Thermodynamic equilibrium
0) A few words about second derivatives of thermodynamic potentials:
Postulate 2 implies that S is maximized at constant U: dS=0, d2S < 0. The second
inequality is required to make sure that the point where the slop i
Part II. Statistical mechanics
Chapter 9. Classical and quantum dynamics of density matrices
Statistical mechanics makes the connection between macroscopic dynamics and
equilibriums states based on microscopic dynamics. For example, while thermodynamics
c
Chapter 10. Postulates of statistical mechanics
Thermodynamics puts constraints on the behavior of macroscopic systems
without referencing the underlying microscopic properties. In particular, it does not
provide a quantitative connection to the origin of
Chapter 13. Other ensembles and fluctuations
1) Other ensembles:
When U, V, n are variables, W(U, V, N) is the partition function. When T, V, N are
variables, Q(T, V, N) is the partition function. By analogy to the Massieu function or
bath derivations out