Philosophy of thermal and statistical physics

The philosophy of thermal and statistical physics is that part of the philosophy of physics whose 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 does statistical mechanics tell us about the arrow of time?

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 over time. In orthodox versions of thermodynamics, properties such as temperature and entropy are defined for equilibrium states only. The idea of the existence of states of thermodynamic equilibrium has been central but tacit to thermodynamics. It has recently been dubbed the "minus first law of thermodynamics".

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 the first three laws of thermodynamics. There is a fourth law, not discussed here.

Two systems are said to be in thermal equilibrium when 1) both of the systems are in equilibrium, and 2) they remain in equilibrium when they are brought into contact, where 'contact' is meant to imply the possibility of exchanging heat, but not work or particles. Thermal equilibrium is:

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