Philosophy of thermal and statistical physics

Philosophy of thermal and statistical physics

The philosophy of thermal and statistical physics is one of the major subdisciplines of the philosophy of physics. Its subject matter is classical thermodynamics, statistical mechanics, and related theories. Its central questions include: What is entropy, and what does the second law of thermodynamics say about it? Does either thermodynamics or statistical mechanics contain an element of time-irreversibility? If so, what is its connection with the arrow of time?

What is thermodynamics?

Thermodynamics is the study of the macroscopic behaviour of physical systems under the influence of exchange of work and heat with other systems or their environment. It is not concerned with the microscopic properties of these systems, such as the movements of atoms.

At the very heart of contemporary thermodynamics lies the idea of thermodynamic equilibrium, a state in which no macroscopic properties of the system change with time. In orthodox versions of thermodynamics, properties such as temperature and entropy are defined for equilibrium states only. The idea that all thermodynamic systems in a fixed volume will reach a state of equilibrium after an infinite time, which is central to thermodynamics, has recently been dubbed the "minus first law of thermodynamics".

Thermodynamics as a theory of principle

Traditionally, thermodynamics has often been described as a "theory of principle". This is a theory in which a few empirical generalisations are taken for granted, and from them the rest of the theory is deduced. According to this view, there is a strong correspondence between three empirical facts and three theoretical laws that lie at the core of the classical theories: the first three laws of thermodynamics.

The zeroth law of thermodynamics

Two systems are said to be in "thermal equilibrium" when 1) both of the systems are in a state of equilibrium, and 2) they remain so when they are brought into contact, where 'contact' is meant to imply the possibility of exchanging heat, but not work or particles. It is an empirical fact, the so-called "zeroth law of thermodynamics", that thermal equilibrium is transitive. This means that whenever system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, then system A and system C are also in thermal equilibrium. According to Max Planck, who wrote an influential textbook on thermodynamics, and many other authors, this empirical principle shows that we can define the "temperature function" so central to our everyday conception of heat.

The first law of thermodynamics

In simplest terms, the first law states that the internal energy level of an isolated system is a constant. In the context of a non-isolated system, then, this law requires that when there is a change in the amount of energy from one equilibrium state to another, that change is equal to the heat transfer into the system minus the work done by the system. Energy in minus energy out equals change in energy level.

"Energy can be neither created nor destroyed"

The second law of thermodynamics

In a general sense, the second law says that temperature differences between systems in contact with each other tend to even out and that work can be obtained from these non-equilibrium differences, but that loss of heat occurs, in the form of entropy, when work is done. This law follows simply from statistics: if a physical system is given (is allowed to occupy) new energy states which are equivalent to the existing states (say, a gas is expanding into a larger volume), then the system will occupy "new" states on equal footing with the existing ("old") ones. This is the central postulate of statistical mechanics - that equivalent energy states are indistinguishable. Thus, as the number of energy states are increasing, the energy of the system will be spread among more and more states (which means that the entropy of the system will increase).

Some have put these latter two laws thus: "The first law says you can't win, the second law says you can't even break even."


There are various ways of understanding this second law. There is, for example, "Boltzmann's H-theorem", an interpretation associated with Ludwig Boltzmann (1844 - 1906).

Maxwell's Demon

James Clerk Maxwell, in an essay in 1871 called the "Theory of Heat," proposed a thought experiment to show why the second law might just be a temporary condition, why entropy might be beatable. This thought experiment was later called Maxwell's Demon.

"If we conceive a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are still essentially finite as our own, would be able to do what is at present impossible for us," he wrote.

He went on to explain that the demon working at a microscopic level, could operate a gate (presumably of low-friction construction) allowing only swift molecules to pass through it. In this way, the demon's work would result in slow molecules (i.e. cold) on one side of the gated barrier, and heat on the other side. Yet movement from uniformity of temperature to a split of hot/cold is in violation of the second law. It follows, Maxwell thought, that the law is just a temporary state of human incompetence. We're not at present capable of treating separately of each molecule that comes by, that's all!

In the 20th century, advances in information theory and thermodynamics eventually determined that Maxwell's demon could not actually reverse entropy, thus disproving Maxwell's approach to violating the second law.


* J. Uffink, "Bluff your way in the second law of thermodynamics," Studies in History and Philosophy of Modern Physics, 32(3), 305-394 (2001)

* P. Valev, "The Law of Self-Acting Machines and Irreversible Processes with reversible Replicas," in D. Sheehan (ed.), Proceedings of the First International conference on Quantum Limits to the Second Law, American Institute of Physics, 430 - 435 (2002):

See also

* Thermodynamics
* Maximum entropy thermodynamics - Bayesian interpretation of thermodynamics, entropy and the Second Law

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