The Fourth Law of Technodynamics

There are three known laws of thermodynamics. Unlike other laws of nature, the laws of thermodynamics were not discovered as a result of studying the nature. They were discovered as a result of studying machines, specifically, thermo machines. They state the necessary conditions of their ability to function.

The first law states that to be able to function, machine has to either consume energy from the environment, or to spend its internal energy.

The second law states that to be able to function, machine has to have both a source and a sink of energy. (It is so called the Kelvin-Planck statement of the second law of thermodynamics.) To have just a source is not enough. There has to also be a sink, which acquires energy from the machine. Energy flows from the source to the sink and machine is in between, exploiting this energy flow. But machine cannot be the sink by itself because it is impossible to fully convert heat into mechanical energy, as Lord Kelvin put it. The level of energy in the source has to naturally be higher than in the sink (otherwise there will be no flow). As machine works the level of energy in the source decreases and in the sink it increases. Specifically for thermo machines, the source becomes cooler and the sink becomes warmer.

The third law states that to take all energy from the source (and thereby to cool it to absolute zero) requires the infinite number of working cycles of the machine (Guggenheim, E.A. (1967). Thermodynamics. An Advanced Treatment for Chemists and Physicists, fifth revised edition, North-Holland Publishing Company, Amsterdam, page 157). Absolute zero cannot be attained in a finite number of operations.

This means that absolute zero is not achievable for a number of reasons:

• infinite number of operations requires infinite time, unless operations are performed progressively faster. The later might be impossible (for example, when progressively faster means progressively faster mechanical speed of machine's parts, as speed of any part cannot exceed the speed of light);
• no machine can perform infinite number of the working cycles without breaking down at some point.

The law can also be interpreted in the opposite way: since absolute zero is not achievable, no machine can perform infinite number of working cycles without completely wearing down at some point.

The above laws of thermodynamics can be considered as laws of technodynamics, a wider discipline that studies the laws of functioning and conditions of workability of any machines, not thermo-machines only. The laws of thermodynamics constitute the first three laws of this new discipline. There are other laws on the top of them, one of which is described below.

The functioning of any machine gradually results in emerging unwanted changes in it. If these unwanted changes (say, wear and tear) exceed some level, the machine ceases to be workable.

Let C(t) be the pace of such unwanted changes in the machine at an instant t. And let T be the duration of the working cycle of the machine. Then for the machine to be workable, the following relationship has to hold:

 T C(t)dt ≤ A, ∫ 0

where A is the level of unwanted changes in the machine, above which it cannot function either at all or as designed.

The meaning of the above relationship is that to be of any utility, a machine has to have time to perform at least one working cycle before it breaks down. In more general terms, it has to have the time to perform at least one working cycle before unwanted changes in it will have reached the threshold after which it cannot function properly (either at all or as designed).

In particular, if C(t) = const, then T ≤ A/C, where A/C is equal to the time required for the unwanted changes in the system to accumulate to the above threshold.

Examples of invention proposals (and even patented inventions) that violated this law and thereby did not work at all or as intended were published here.