# Conflict between a system lowering its potential energy and kinetic energy

Every system in the universe has a natural tendency to attain a state of minimum energy. The state of minimum energy corresponds to a state of maximum stability.

These are from a renowned book. I am facing some problems in accepting this statement.
From the law of conservation of energy I can conclude that a decrease in potential energy must be accompanied with an increase in kinetic energy. So why is it that every system wants to decrease potential energy and not kinetic energy? Matter we see around us could have split into constituent particles with infinite separation but why does that not happen?

Infinite separation is not the minimum potential energy that can be achieved but why does the system wants to minimize its potential energy and not kinetic energy? For better understanding considering this: a ball is dropped from a tall building. It lowers its potential energy with an subsequent increase in kinetic energy and hits the surface. Now revert the clock back. The ball moves from the surface to the top of the building with its velocity gradually decreasing(N.B. The direction of velocity is downwards). This process of course violates fundamental definitions like $$\vec{a} = \frac{d\vec{v}}{dt}$$ but is energetically favourable. I favour energy conservation before anything else because it reduces calculations and simplifies problems. But why does it fail in this case?

• Decrease in potential energy is not always accompanied by an increase in kinetic energy. The system can release potential energy and fall back to a lower energy state. E.g. when an electron jumps to lower energy level, the drop in potential energy is released as em radiation. Commented Oct 6, 2021 at 6:11

Good question. TL;DR: saying that systems want to minimize energy is some kind of heuristic, but it is not a true law.

The statement that systems have a tendency to lower their energy is a sloppy rephrasing of the second law of thermodynamics which favours disorder i.e. homogeneous distribution of energy across all degrees of freedom (DOF). And in the approximation here, the system is interacting with an environment which has an infinite amount of such DOF.

More technically, when a system can exchange energy with such an infinite environment (also 'bath' or 'reservoir'), given any absence of driving that prevents it from reaching equilibrium, it will strive towards a configuration that minimizes the free energy

$$F=E-TS$$

where $$E$$ is the system's energy, $$T$$ the temperature of the bath and $$S$$ the entropy. For macroscopic systems at room temperature, the second term is often negligible.

Note that the situation is different in isolated systems that cannot exchange energy with their environment (dissipation), then there is no relaxation and energy is solely exchanged between potential and kinetic. The typical example is a pendulum, which would go on oscillating forever in absence of such dissipation. Also for example for the solar system, we are lucky that there is no efficient channel for the earth to dissipate its gravitational energy, otherwise we would collapse into the sun.

• I am a beginner and find it difficult to generalise laws of Thermodynamics to other fields. All that I know from the second law is that the entropy of the universe always increases in the course of every spontaneous change and the spontaneity of a process is determined by the Gibbs Helmholtz Equation $$∆G = ∆H - T∆S$$ where $∆G$ is change in Gibbs energy. I have learnt that enthalpy change $∆H$ is the measure of heat change taking place during a process at constant pressure. Due to this I am unable to generalise this fact. Please explain the same in the answer. Commented Oct 6, 2021 at 14:20
• Hi @SDas the equation you are mentioning is in essence the same, except the functionals G, H are defined for fixed pressure instead of fixed volume. Similarly, F and G are defined for fixed temperature and E,H for fixed entropy. See also en.wikipedia.org/wiki/Thermodynamic_free_energy . Technically, the transformation of going from one to the other is called a Legendre transform. The fact that entropy S is used in these formulas may be confusing. It relates to the system only; and does not need to increase as does the total entropy of the universe; Commented Oct 7, 2021 at 2:05