Laws of thermodynamics

The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. Since their conception, however, these laws have become some of the most important in all of physics and other branches of science connected to thermodynamics. They are often associated with concepts far beyond what is directly stated in the wording.

History
The first established principle of thermodynamics (which eventually became the Second Law) was formulated by Sadi Carnot in 1824. By 1860, as found in the works of those as Rudolf Clausius and William Thomson, there were two established "principles" of thermodynamics, the first principle and the second principle. As the years passed, these principles turned into "laws." By 1873, for example, thermodynamicist Josiah Willard Gibbs, in his “Graphical Methods in the Thermodynamics of Fluids”, clearly stated that there were two absolute laws of thermodynamics, a first law and a second law.

Presently, there are a total of five laws. Over the last 80 years or so, occasionally, various writers have suggested adding Laws, but none of them have been widely accepted.

Overview

 * Zeroth law of thermodynamics
 * $$A \sim B \wedge B \sim C \Rightarrow A \sim C$$
 * First law of thermodynamics
 * $$\mathrm{d}U=\delta Q-\delta W\,$$
 * Second law of thermodynamics
 * $$\oint \frac{\delta Q}{T} \ge 0$$
 * Third law of thermodynamics
 * $$ T \rightarrow 0, S \rightarrow C $$
 * Onsager reciprocal relations - sometimes called the Fourth Law of Thermodynamics
 * $$ \mathbf{J}_{u} = L_{uu}\, \nabla(1/T) - L_{ur}\, \nabla(m/T) \!$$;
 * $$ \mathbf{J}_{r} = L_{ru}\, \nabla(1/T) - L_{rr}\, \nabla(m/T) \!$$.

Zeroth law
"If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other."

When two systems are put in contact with each other, there will be a net exchange of energy between them unless or until they are in thermal equilibrium, that is, they contain the same amount of thermal energy for a given volume (say, 1 cubic centimeter, or 1 cubic inch.) While this is a fundamental concept of thermodynamics, the need to state it explicitly as a law was not perceived until the first third of the 20th century, long after the first three laws were already widely in use, hence the zero numbering. The Zeroth Law asserts that thermal equilibrium, viewed as a binary relation, is an equivalence relation

First law
"In any process, the total energy of the universe remains the same."

It can also be defined as: "for a thermodynamic cycle the sum of net heat supplied to the system and the net work done by the system is equal to zero."

More simply, the First Law states that energy cannot be created or destroyed; rather, the amount of energy lost in a steady state process cannot be greater than the amount of energy gained.

This is the statement of conservation of energy for a thermodynamic system. It refers to the two ways that a closed system transfers energy to and from its surroundings - by the process of heating (or cooling) and the process of mechanical work. The rate of gain or loss in the stored energy of a system is determined by the rates of these two processes. In open systems, the flow of matter is another energy transfer mechanism, and extra terms must be included in the expression of the first law.

The First Law clarifies the nature of energy. It is a stored quantity which is independent of any particular process path, i.e., it is independent of the system history. If a system undergoes a thermodynamic cycle, whether it becomes warmer, cooler, larger, or smaller, then it will have the same amount of energy each time it returns to a particular state. Mathematically speaking, energy is a state function and infinitesimal changes in the energy are exact differentials.

All laws of thermodynamics but the First are statistical and simply describe the tendencies of macroscopic systems. For microscopic systems with few particles, the variations in the parameters become larger than the parameters themselves, and the assumptions of thermodynamics become meaningless. The First Law, i.e. the law of conservation, has become the most secure of all basic laws of science. At present, it is unquestioned.

Second law
"The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium."

In a simple manner, the second law states that "energy systems have a tendency to increase their entropy" rather than decrease it.

A way of looking at the second law for non-scientists is to look at entropy as a measure of chaos. So, for example, a broken cup has less order and more chaos than an intact one. Likewise, solid crystals, the most organized form of matter, have very low entropy values; and gases, which are highly disorganized, have high entropy values.

The entropy of a thermally isolated macroscopic system never decreases (see Maxwell's demon). However, a microscopic system may exhibit fluctuations of entropy opposite to that dictated by the Second Law (see Fluctuation Theorem). In fact, the mathematical proof of the Fluctuation Theorem from time-reversible dynamics and the Axiom of Causality constitutes a proof of the Second Law. In a logical sense the Second Law thus ceases to be a "Law" of physics and instead becomes a theorem which is valid for large systems or long times.

The first and second law can be combined to yield the Fundamental Thermodynamic Relation:

$$dE = TdS - pdV\, $$

Here, E is energy, T is temperature, S is entropy, p is pressure, and V is volume.

Third law
"As temperature approaches absolute zero, the entropy of a system approaches a constant minimum."

In brief, this postulates that entropy is temperature dependent and leads to the formulation of the idea of absolute zero.

Tentative fourth laws or principles
In the late 19th century, thermodynamicist Ludwig Boltzmann argued that the fundamental object of contention in the life-struggle in the evolution of the organic world is 'available energy'. Since then, over the years, various thermodynamic researchers have come forward to ascribe to or to postulate potential fourth laws of thermodynamics; in some cases, even fifth or sixth laws of thermodynamics are proposed. The majority of these tentative fourth law statements are attempts to apply thermodynamics to evolution. Most fourth law statements, however, are speculative and far from agreed upon.

The most commonly proposed Fourth Law is the Onsager reciprocal relations. Another example is the maximum power principle as put forward initially by biologist Alfred Lotka in his 1922 article Contributions to the Energetics of Evolution. Most variations of hypothetical fourth laws (or principles) have to do with the environmental sciences, biological evolution, or galactic phenomena.

Extended interpretations
The laws of thermodynamics are sometimes interpreted to have a wider significance and implication than simply encoding the experimental results upon which the science of thermodynamics is based. See, for example:
 * Principles of energetics
 * Heat death