I say holistic because it concerns entropy, thermodynamics. NB. I do not suggest extensive knowledge of thermodynamics but I am learning. To the question!!! The universe is expanding and thus can be considered boundless. (I know I have made assumptions but they are based on a lack of evidence to refute, however I am aware that this could easily be due to insufficient research) The resultant rate of expansion is increasing. Thus the entropy of the universe will increase indefinitely. If I am wrong so far, feel free to KO this thread. I have issues with the conclusion reached above 1.The more entropy a system has the colder it is. 2.There is a limit to how cold something can be. 3. That which has a temperature approaching infinty is perfectly ordered or is approaching perfect order. I will elaborate Number one would by extension, suggest that a boundless system may become infinitely cold or approach such a state of existence, number two refutes this, however both one and two can be correct based on what was stated about the expansion of the universe. Number three suggests that the total enthalpy of every system in the universe is infinite, as this would have been necessary for the universe to have initially been perfectly ordered. Please explain and ease my confusion.
To add to UltrafastPDE post - imagine having two identical tanks, separated by a valve. One contains one gas, other contains other gas. To make things as simple as possible both have the same volume, the same pressure, the same temperature. You open the valve: 1. What happens? 2. Does the temperature change? 3. Does the entropy change?
But these aren't boundless systems. In a boundless system surely an increase in entropy will decrease the temperature, as temperature is the heat energy in a given volume.
Entropy increases with the number of microstates available; you will find a nice tutorial here: http://entropysite.oxy.edu/microstate/ Also it is not clear that the universe is "boundless"; according to General Relativity it has a finite volume, though this is expanding.
Sorry I did not mean to say that the universe is, at the presenet, boundless I just mean that it is getting larger, but I will also say, those bodies that make up the edge of the universe are stated to have a greater velocity than the bodies Which approach them from the center of the universe, all bodies are also all accelerating, in that sense the boundaries will never be met. If the boundaries can never be reached can the system be considered to have boundaries even if it's volume is finite. Thanks for the link!
You can find excellent answers to many of these questions here: http://www.astro.ucla.edu/~wright/cosmology_faq.html And yes, a system can have a finite volume even if the "edges" are outside of your light cone. The two concepts are independent. For example consider if you had just fallen through the event horizon of a monster black hole: it has a finite volume, but you can no longer reach the event horizon.
Thank you for the link. I wasn't suggesting that the volume was infinite if the boundaries could not be reached I was suggesting that despite the fact that the volume is finite the system is boundless from my perspective. In the case of a black hole the event horizon is dependent on the velocity of the consumed body, whereas in the case of the universe the edges are defined by the position of the bodies not necessarily their velocity. EDIT: How is the volume of a black hole determined?
This is incorrect; the event horizon is a relativistic invariant quantity, as is the mass and surface area. However the volume is not a relativistic invariant, so you get different answers with different choices of coordinates. This is discussed in detail here: http://physics.stackexchange.com/questions/45963/do-black-holes-have-infinite-areas-and-volumes Thus we usually don't talk about the volume of a black hole ... under our current theories it is not possible to define it.
A few snipes here: Defining volume relativistically is a bit tricky here. A spatial volume is one component of a space-time tensor. In GR one can define distinct "world sheets" to stand in as "the universe right now" which have different spatial volumes. Defining "The Universe" too can get a bit tricky w.r.t. thermodynamic systems. Finally when you get down to the quantum level Entropy is sub-additive and not additive in that the entropy of a whole system can be less than the entropy of the parts... entropy is not a "substance" and we error in applying substance-like intuitions to it... including adding up the whole from the pieces. I am fond of exclaiming "The entropy of the universe is zero!" to emphasize this in the extreme and to underline the flaw in thinking at all about "the entropy of the universe" as a whole. Some specifics to your question: you can define negative temperatures but they are not simply the result of "passing zero" rather it is reciprocal temperature which is more directly definable in thermodynamics and the T=0, 1/T=infinity horizon is only asymptotically approachable. You're statement about infinite temperature doesn't make sense to me, where did you get that? Finally entropy has nothing to do with "order" or "disorder" which are value judgements. One might as well say it has to do with "how pretty" the system is. Entropy has to do with knowledge about the system (which is not a judgement but the result of specific observations and/or constraints applied physically to the system). In physics "knowledge" has been specifically defined to be empirical knowledge and hence its possession has specific physical implications since you must physically interact with and/or constrain a system to have such empirical knowledge. Note, we can know that parts are correlated (quantum entanglement) without knowing specifics about each part which may be nonetheless maximal knowledge about the whole. The entropy of each part may add to more than the entropy of the whole. Another valid definition of entropy is as a measure of the entanglement of a system with its environment (and hence the entropy of the universe = 0 since it has no "environment" with which to entangle. That however is not to be confused with "the observable universe" and we can get into scenarios where we entangle with objects in-falling into black holes and the whole space-time world sheets issue gets back into the game.)
Thanks. Btw when I said infinite temperature I was referring to an infinite amount of heat/or an infinitesimally small volume over which that heat energy is distributed. When I said the the event horizon is dependent on velocity I just meant that if the potential velocity of the consumed body exceeded that of light then the event horizon would be closer to the singularity, similary if the consumed body did not have the potential to achieve a velocity even half that of light then the event horizon would be further from the singularity. I understand though that as no such body is known to exist the event horizon for light is taken as universities. I just mean that it is conceptual.