We have introduced Thermodynamics using a statistical, quantum-based
approach and have not relied on postulates. However, historically
Thermodynamics was analyzed in terms of four separate unverified
statements known as the Laws of Thermodynamics. We have more tools
to verify the statements, though, and you may be surprised at the
simplicity of the laws.

###
Zeroth Law

The Zeroth Law supposes that we have three systems in which the first
two are each in thermal equilibrium with the third. Then the Law claims
that the first two are likewise in thermal equilibrium with each other.
Recall that the equilibrium condition was that the temperatures be
equal. Then we have: If *τ*_{1} = *τ*_{3} and *τ*_{2} = *τ*_{3} then
*τ*_{1} = *τ*_{2}. It isn't hard to see why this is so.

###
First Law

The First Law has many formulations. Historically, the Law is stated as
such: the work done in taking an isolated system from one state to
another is independent of the path taken. We know from previous study
of mechanics that energy behaves the same way. It turns out that this
work can be called heat, and therefore a sleeker definition of the First
Law is: Heat is a form of energy. The path independence follows from
this simple statement.

###
Second Law

The Second Law has an overwhelming number of formulations. We shall
present two here, one that makes sense given the statistical origins
we've focused on, and one that has historical value and will be useful
later when we deal with engines.

Statistically, we say that: if a closed system is not in equilibrium,
then the most probable future is that the entropy will increase with
each passing bit of time, and will not decrease. The more foreign
formulation, useful later (see Heat, Work, and
Engines), known as the Kelvin-Planck
formulation, is: it is impossible for any cyclic process to occur whose
sole effect is the extraction of heat from any reservoir and the
performance of an equivalent amount of work. The popularized version of
the second law looks more like the first explanation and has been
recently challenged by considerations of the physics of black holes.

###
Third Law

Qualitatively, the Third Law claims that as a system approaches absolute
zero, or *T* = 0, it becomes increasingly ordered, and thus exhibits a low
entropy. Strictly, we say that: the entropy of a system approaches a
constant value as the temperature approaches zero. This constant value
is near or at zero, usually. Consider a system with a non-degenerate
(i.e. having a multiplicity function value of one) ground state. Then
the entropy of that state is zero. As the temperature decreases, the
system becomes more and more likely to be found in the ground state, as
we shall see in Statistics and Partition
Function. Thus the entropy will
approach a small, near zero value.