Entropy, given in equations as the symbol, is defined then as The total phase space of a system will have many regions all of different shapes and sizes and could look like the followingīut how is all this abstract representation linked to entropy. So in the phase space we could put a box around the 16 states that defines all the states inside it as being macroscopically indistinguishable.
These 5 layouts of the 4 particles, along with the 11 other combinations, make up a set of states that are (apart from the colours) indistinguishable. If we add these to the phase space along with the original we get something like Each of these set-ups will correspond to a different position in phase space as they are all different layouts of the system of the 4 particles. In terms of the system, there are multiple other combinations of the 4 particles that will be as organised as the above stateĪnd so on. If we imagine the case where all of the particles are located in one corner of the container then we have the situation If we imagine that each of the particles is a different colour so we can keep track of their positions easier. For our purposes we will not need to consider the dimensions. In all the diagrams I will depict the phase space as 2D to make it easier to convey what it actually represents. So in our case, the phase space is 12 dimensional, in order that each point can describe the location of 4 bodies. In our example we are only interested in the positions of the 4 particles, so each point in phase space must contain an x, y, and z co-ordinate for each particle so our phase space is 3N dimensional, where N is the number of particles in the system. Each point in the phase space for this system tells you where all 4 balls are located in the box. Imagine I have a box with 4 gas particles inside. Some of the concepts for this may be a bit confusing but bear with me, once you’ve got your head round it it’s not that bad.Ī phase space is just like a graph, but a point on this graph represents the whole state of a system. To get a more detailed picture of entropy we need to look at the concept of Phase Space. As it moves through the air however, some of the kinetic energy is distributed to the air particles so the total entropy of system has increased (the total energy is conserved however, due to the first law)
Essentially entropy is the measure of disorder and randomness in a system. It’s the core idea behind the second and third laws and shows up all over the place. Entropy and Phase SpaceĮntropy is a very important thing in the realm of thermodynamics.