Clausius put forward the principle of conservation of energy, that is, the first law of thermodynamics, in the article On the power and energy of heat and the law of heat itself, and it has been developing continuously. The principle of conservation of energy is expressed as follows: the change of total energy of a system can only be equal to the amount of energy transmitted into or out of the system. Total energy is the sum of mechanical energy, thermal energy and any form of internal energy except thermal energy.

After the first law of thermodynamics came out, people realized that energy could not be generated out of thin air, so the first perpetual motion machine went bankrupt, so someone proposed to design a device to absorb heat energy from the ocean, atmosphere and even the universe, and use this heat energy as the source of driving the perpetual motion machine to rotate and output power, which is the second perpetual motion machine.

At this time, some limitations of Newton's classical mechanics are exposed. For example, Newton's classical mechanics thinks that the mechanical process is reversible, and reversibility refers to the reversal of time, that is, the process is carried out in the opposite order. In the equation of motion of classical mechanics, changing the time parameter t to -t means that the process goes through all the initial states in reverse order and finally returns to the initial state.

At this time, in 1850, Clausius and Kelvin re-examined Carnot's theorem after the first law of thermodynamics was established, and realized that Carnot's theorem must be based on a new theorem.

1824, the young French engineer Carnot studied the efficiency of the ideal heat engine by using the concept that perpetual motion machine is impossible to realize. The cycle process of this heat engine is called Carnot cycle. So Carnot principle is put forward: the efficiency of irreversible heat engine is always lower than that of reversible heat engine working between the same two heat sources, and the efficiency of all reversible heat engines working between the two heat sources is the same.

British physicist Kelvin found some incongruities when he studied the work of Carnot and Joule: according to the law of conservation of energy, heat and work should be equivalent, but according to Carnot's theory, heat and work are not exactly the same, because work can be completely converted into heat without any conditions, and heat must be accompanied by dissipation from heat to cold.

In the theory of heat, besides the law of conservation of energy, another basic law must be added: "Without some kind of power consumption or other changes, it is impossible to transfer heat from low temperature to high temperature." This law is called the second law of thermodynamics. The second law of thermodynamics contradicts the reversibility of mechanical processes.

In short, the entropy of an isolated system never decreases automatically, remains unchanged in the reversible process and increases in the irreversible process, which can be said to point out the direction of the irreversible process very clearly. It shows that the reversibility of classical mechanics is not applicable to all cases, and it is accurate only when it is guaranteed by universal mechanical principles. Thermal motion is an irreversible process.

The law of entropy increase is considered to be the law that makes the whole universe desperate. Not only can black holes escape the law of entropy increase, but so can the universe.