The concepts of thermodynamics have been presented in a classical way in
terms of the laws of thermodynamics and fundamental concepts such as
Gibbs energy and entropy. These same central concepts can also be explored
from the more mathematical foundation of statistical thermodynamics.
The statistical approach is capable of reproducing the thermodynamic
properties of matter from a microscopic viewpoint. Systems are described
in terms of the probabilities of different states that are described by the
Boltzmann distribution and partition functions. A particular usefulness
of this approach is its ability to provide a formal definition for entropy.
The description of objects in terms of distributions is useful for under-
standing biological systems that involve multiple states, such as proteins
as they fold, and that can exist in more than one conformation, as found
for prions.
Probability
Probability theory was developed in the late 1600s as a formalism to describe
games of chance. In probability theory, variables are quantities that can
change in value throughout a series of events. Discrete variables can assume
only a limited number of specific values. For example, the outcome of a
coin toss is one of two possibilities, heads or tails. Once the variables are
established, the goal is to determine the probability that a variable will
have a certain value. Probabilites are defined such that for any given event
with ipossible outcomes, each of which has a probability Pi, the sum of
all probabilities is one:
(8.1)
Pi
i∑ =^1