The first rigorous definition of the second law based on the concept of entropy came from German scientist Rudolf Clausius in the 1850s and included his statement that heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time. Its first formulation, which preceded the proper definition of entropy and was based on caloric theory, is Carnot's theorem, formulated by the French scientist Sadi Carnot, who in 1824 showed that the efficiency of conversion of heat to work in a heat engine has an upper limit. The second law has been expressed in many ways.

Statistical mechanics provides a microscopic explanation of the law in terms of probability distributions of the states of large assemblies of atoms or molecules. Historically, the second law was an empirical finding that was accepted as an axiom of thermodynamic theory. An increase in the combined entropy of system and surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time. The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always tend toward a state of thermodynamic equilibrium where the entropy is highest at the given internal energy. For example, the first law allows the process of a cup falling off a table and breaking on the floor, as well as allowing the reverse process of the cup fragments coming back together and 'jumping' back onto the table, while the second law allows the former and denies the latter. It predicts whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes. The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. Another statement is: 'Not all heat can be converted into work in a cyclic process.' A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient).

Published August 5, 1925.The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. Incidentally, we shall also show that different crystalline forms of a substance have the same entropy at the absolute zero, irrespective of the number of atoms in the unit of structure of the crystal, in contradiction to the suggestion recently made by Eastman that the entropy is greater, the larger the number of atoms in the unit cell.

Indeed, we shall be able to show that the excess entropy of a glass is related in a simple and definite manner to the properties of the glass when regarded as a quantum system with its degrees of freedom in the next to the lowest quantum state. We shall in this way obtain a more precise idea of the factors which can make the entropy of a supercooled liquid or glass greater than that of the corresponding crystal. The purpose of the present article is to investigate the entropy of supercooled liquids at the absolute zero by the methods of statistical mechanics.

What is the entropy at absolute zero