# Ordered and random energy [closed]

One of the books refer to potential energy being ordered whereas heat energy being random. Could someone explain what is ordered and random energy?

• A falling object moves in one direction, and only one : downwards. A pendulum may move in two directions : North-South and/or East-West or a combination of both. It has two degrees of freedom. Its movement is more random than a falling object. If now the pendulum hangs at a rubber band, it gets a third degree of freedom : up-downwards. Its movement is still more random. A hot body is made of particules that can move or vibrate like my elastic pendulum. It has three degrees of freedom. Its movement is more random. Apr 1 at 8:33
• Ordered and random energy is merely an abuse of language. Apr 1 at 8:50
• Imagine a group of children at a summer camp trying to pick up a heavy wooden log/trunk a) orderly by command b) randomly. The present energy is the same, but in the latter case of less use or even useless. That is like the case of the thermal energy, than can be directly use as the energy source only by balancing temperature with a colder object. For other cases, you need other primary energy source to pump this energy in thermal pumps. Apr 1 at 14:32
• Such a textbook should not be used which propagates wrong ideas. Apr 1 at 15:51
• Could you provide passages (quotes) from the textbook that explicitly refer to "ordered" and "random" energy? Apr 3 at 8:00

Consider the ability to predict something in a detailed manner as synonymous with "ordered", and the inability synonymous with "random". For instance, a perfect crystalline solid is more ordered than a gas because given the position of one particle in a solid and a few lattice constants we can derive to a good extent the positions of all particles in the solid. In a gas, knowing the position of one particle constrains the maximum distance of all others (given the temperature and pressure) and with some additional parameters provides perhaps a distribution function for the particles, but we can say little more about where the other particles actually are (we might say something detailed however about where they might be).

Consider an analogy useful to get physical intuition into why we might really refer to a system as "ordered" or "random". Consider a system of many balls colliding elastically. Up to some number of balls we can describe the motions of the balls with a high level of detail and maybe even predict future trajectories. We would consider this a relatively orderly process. But if the balls become too many, then we give up and instead try to describe the statistical properties of the collection of balls, and say the balls move randomly.

Usually one speaks of a system being ordered or a configuration being random, but not about energy itself. However, heat can be understood as energy being transferred through the random motion of particles, whereas work involves coherent motion of the same particles (in a gas some of the molecules happen to move coherently, that is, in what looks like an orderly parallel displacement. These are responsible for work). In that sense one might describe heat as involving a transfer of "random energy" and work as being a transfer of "ordered energy".

So what decides whether you call something random versus ordered (or heat or work) is then how much information you have to describe the system. The idea is that describing the detailed motion (positions and momenta) of a very large numbers of things, on the order of $$\pu{6E23}$$ particles (moles of stuff), and on top of that as a function of time, is difficult (actually it's impossible). So instead of even trying we speak of "heat" as the energy that is exchanged by all those particles when they collide with each other in ways we can't measure or predict in detail. We say that their motion is random, which is shorthand for saying we can't describe their motions except perhaps in a statistical sense, using measures such as entropy. Work (and change in potential energy) on the other hand is something we can measure in detail, because we use things such as volumes and distances of large objects to describe it. For instance when a gas expands we can measure how much the volume changed against an externally applied pressure (force per unit area). So we call this an orderly process, even though the molecules in the gas that do the work are moving about in individually undescribable ways.

Another example is the solar system versus a galaxy. The solar system does not appear random because we can describe the motions of the sun, planets and other large objects in great detail, and sometimes predict their motion far into the future. OTOH when we look at a galaxy the large number of objects make a detailed description more challenging, and it can be useful to use statistical measures to describe the collection of objects and just say that the distribution of stars looks pretty random. See for instance Ref 1 (the following from the introduction):

Except for interacting galaxies, it is reasonable to suppose that elliptical galaxies are, at least, objects in thermodynamic quasi-equilibrium (the best evidence being the regularity in the luminosity distribution). Hence we will proceed by computing the entropy of a self-gravitating system using classical thermodynamics. Let us assume that the stars in a galaxy behave like an isolated, self-gravitating gas of equal-mass particles. Consequently, we start by taking the differential of the entropy: ...

Reference

1. G. B. Lima Neto D. Gerbal and I. Marquez. The specific entropy of elliptical galaxies: an explanation for profile-shapedistance indicators?Mon. Not. R. Astron. Soc.309, 481±495 (1999)