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Expansion of the Universe and Thermodynamics

  1. Dec 28, 2015 #1

    I have a very basic question about the expansion of the Universe and it could be that I'm being very stupid here: if the universe is expanding into the empty surroundings as the red shift evidence seems to demonstrate, then surely the universe must be doing work on the surroundings like a gas expanding freely against a massless piston. However we also know that the universe is likely flat and therefore has zero internal energy which is constant with time. According to the first law of thermodynamics we therefore have Delta U = 0 = W + Q, where W is negative since work is being done by the system (the universe) against the surroundings..... does that mean that there is a positive heat (Q) entering the system from the surroundings? In that case how can heat come from the void region around the universe which has no energy whatsoever??


    Gabriele Mogni
  2. jcsd
  3. Dec 28, 2015 #2


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    Work is pressure times distance. Since the pressure is zero (there's nothing out there) no work is done on the surroundings.

    Come to think of it, there's no surroundings either ... o_O

    And: no, it's not a stupid question at all !
  4. Dec 28, 2015 #3


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    The universe is not expanding into empty surroundings. It is space itself that is expanding. Distances are becoming larger, but nothing really needs to "move". (I put move in quotations because this is a relative thing, here defined by moving relative to the cosmic comoving frame.)
  5. Dec 28, 2015 #4


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    I'm glad to have been put right on this issue! I'm an experimentalist and my mind boggles with these questions. At least I can claim I sensed something was warped :smile:. And with me it still is o_O.
  6. Dec 28, 2015 #5
    Pressure only has any particular relevance when there is a comparison between two pressures.

    Despite what is mentioned above, and although indeed, there is no "external" pressure to the universe, however, positive and negative energy contributions can act in a manner which would be measurably identically to pressure differences.
    Therefore, positive contributions within the universe (such as those via gravity) by result are identical to a comparison whereby external pressure is greater than internal, and the negative energy contributions (i.e. Dark Energy) have a result that mimicks a situation where external pressures would be less than the internal.
  7. Dec 28, 2015 #6
    But when you think of a gas expanding freely against a massless piston then it's the internal pressure of the gas that matters, not the external pressure of the surroundings, and the universe certainly has pressure since it's like a hot gas!

  8. Dec 28, 2015 #7
    Think of the standard equation for the work dW=-pdV https://www.grc.nasa.gov/www/k-12/airplane/work2.html).....From [Broken]From my (rusty) memories of undergrad Thermodynamics and books like Adkins the p term is the internal pressure of the gas which is only equal to the external pressure of the surroundings if the system and surroundings are in equilibrium with one another and nothing moves. After all think of a situation where a gas is suddenly let loose by removing all the weights on a piston and the gas begins expanding freely from an initial pressure p against the piston and surroundings at zero pressure, the gas still does work against the surroundings which is given by $\Delta W = - \int{pdV}$.

    If the universe is indeed expanding then its pressure is probably decreasing with time until one day it will reach zero or even become negative at which point the universe will start contracting.....

    Last edited by a moderator: May 7, 2017
  9. Dec 28, 2015 #8
    With the example of a massless piston, there is something behind the piston providing a reactive force. The difference betwee the force from the gas expansion and the 'presumably also gaas) BEHIND the piston results in the measured pressure difference resulting in the piston's movement.

    The gas 'expands' as a result of the "particles" having degrees of freedom and momentum giving rise to the 'pressure'/temperature and the most likely, energetically preferred situation of tending towards a low entropy, ordered state whereby the dispersion between the component "particles" increases.

    The universal expansion is not driven by this motion of particles within spacetime - the spacetime fabric itself (the medcium in which the energy and matter 'reside' is stretching. As mentioned, the effect of the stretching appears and is measurably similar to that of pressure differences, but instead of a difference between an internal and external pressure - instead it is the internal POASITIVE and internal NEGATIVE "pressures" that produce the difference.
  10. Dec 28, 2015 #9
    So what is the result of this pressure balance? Do you believe that the universe still has net positive pressure? In that case I still struggle to understand the difference between the expansion of the universe and the free expansion of a gas, since in none of the examples of gas expansion given in thermo books do they say anything about the nature of the vacuum in the surroundings.... we might just well assume it's a perfect vacuum with zero pressure just like the surroundings of the universe....

  11. Dec 28, 2015 #10
    "There is a growing consensus among cosmologists that the universe is flat and will continue to expand forever.[2][3] The ultimate fate of the universe is dependent on the shape of the universe and what role dark energy will play as the universe ages."

    Then surely the net total pressure of the universe is positive, i.e. the positive pressure contributed by Gravitational forces is greater than the negative pressure generated by Dark Energy (I hope this makes sense).......
  12. Dec 28, 2015 #11

    My question arose from the above presentation where the Presenter makes the case that the Big Bang did not violate conservation of energy since we went from a state of zero energy before the universe to another state of zero energy thanks to the zero curvature of the universe whereby negative gravitational potential energy exactly cancels out positive kinetic energy. If it was true that Big Bangs come with zero energy cost and only require some simple quantum fluctuations, how come they don't happen all the time in vacuum chambers here on Earth?? Surely there must be another massive energy requirement for Big Bangs which has not been taken into account.....
  13. Dec 28, 2015 #12


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    Let's make sure here that it is clear, that the expansion of the universe is not driven by the gas pressure of matter in the universe - that moment you indicate, when the universe was filled with gas that could interact thermodynamically outside local domains is long gone. All the gas is contained in the universe is now confined to distinct, gravitationally-bound 'islands' of matter (i.e. clusters of galaxies), with little interaction between each other other than the global curvature effects.
    I.e., one cluster doesn't 'feel' the pressure of gas in the other cluster, since none of the molecules can ever escape the confines of local gravitational wells.

    What drives the expansion of the universe, is the curvature of space-time, which is determined by its contents, and which 'tells' objects what it means to be in free fall (i.e., in curved space-time objects initially at rest may move closer together or further apart).

    In other words, you get the expansion from GR, not from the ideal gas law.
  14. Dec 28, 2015 #13

    But surely an expansion of the universe requires work to be performed on surroundings even if it is not given simply by -pdV and the ideal gas equation of state... surely the expansion of the universe can't violate the laws of thermodynamics!
  15. Dec 28, 2015 #14
    The laws of physics as we know them are constructs of the universe - they apply only within the universe and the matter/energies within the universe.

    Again, there are no surroundings.*

    You are mistaking the description of one concept (ideal gas expansion in a vacuum) as analogous to the apparent motion of matter within the universe due to the expansion of the spacetime itself - with the actual description which is GR providing relative accelerated motion due to gravitational field strength determined by the topography of spacetime being pushed by dark energy.

    I made similar issue with the notion of 'spacetime flowing' into Black Holes - fortunately, someone nicely pointed out the analogy was only accurate in one sense and so was invalid for applying in other areas. Something similar, I believe is the case here.

    *Not entertaining any consideration for hyperdimensional multiverse theories or outlandish conjectures
  16. Dec 28, 2015 #15


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    It's possible to do this kind of analysis using a co-moving volume as your unit (co-moving means that the box expands with the universe), with a hypothetical box surrounding that volume. It is possible to derive how the energy of that volume changes over time by measuring the work done on the "walls" of this box.

    For example, while the universe is radiation-dominated, the pressure on the "walls" is outward while the universe is expanding outward. So because the stuff inside the box is doing positive work to the "walls" of the box, the energy of the stuff inside drops. Similarly, if the universe is dominated by dark energy, then the pressure on the walls is inward, so that the total energy inside the box tends to grow over time. This calculation yields the correct result.

    This kind of calculation isn't useful, however, if you're trying to talk about the entire universe, as not only can you not define an energy for the entire universe, but there is no outside for the universe to push on.
  17. Dec 28, 2015 #16
    There is an interesting discussion supporting this perspective here:
    [I usually like Rovelli papers because they seem to be so clearly worded.]

    Why all these prejudices against a constant?
    Eugenio Bianchi, Carlo Rovelli

    I recently saw a different perspective, from a thermodynamic viewpoint, involving degrees of freedom between an interior bulk and its surface and equipartition theory. What was supposedly shown was that Einstein's GR can be developed from thermodynamic underpinnings, and vice versa; the paper claimed they are two sides of the same coin. Very relevant to the current discussion. If anybody can provide a link, please do. I'll try to find the discussion as well.
  18. Dec 28, 2015 #17
    GR can be described with degrees of freedom in certain abstract spaces. Those same degrees of freedom can then be representative of entropy or entropic capacity if you will.
    Along with the 'usual' debate about the early universe conflicting with a low entropy state and the lack of an entropic description of gravitational fields though, there's not really much to go on. Roger Penrose in "Cycles Of Time" gives a pretty good overview of something similar.
  19. Dec 28, 2015 #18
    The discussion I sought starts here:

    [It is "not open for further replies".....unsure why. ]

    Chronos: "Padmanabhan may have published his most brilliant, or misguided paper to date -http://arxiv.org/abs/1207.0505. This idea looks pretty solid to me." July 2012
    I wonder what has taken place since? like how many citations this and rleated papers have acquired.

    Authors:T. Padmanabhan
    (Submitted on 2 Jul 2012)
    Abstract: ..... In the second part, I describe a novel way of studying cosmology in which I interpret the expansion of the universe as equivalent to the emergence of space itself. In such an approach, the dynamics evolves towards a state of holographic equipartition, characterized by the equality of number of bulk and surface degrees of freedom in a region bounded by the Hubble radius.....This principle correctly reproduces the standard evolution of a Friedmann universe.

    This bulk volume is taken to be the Hubble volume in which the enclosed bulk space is taken to be the cosmic space that has already emerged; The surface is the Hubble sphere. The emergence of matter [degrees of freedom] along with cosmic space occurs during the current expansion era when the universe is making the transition from one de Sitter phase to another.

    Jacobsen puts it this way: "...the Einstein equation is an equation of state..." referring to 'horizon thermodynamics'
  20. Dec 28, 2015 #19


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    Inspire database shows 37 citations on this one:
    of which 12 are self-citations (Padmanabhan citing his own paper)
    If I'm reading the citation history graph right, it says:
    2012 7
    2013 17
    2014 7
    2015 5

    My quick impression was that the papers that cited this one rarely got cited much themselves unless they were by Padmanabhan himself (he's a prominent guy and his papers tend to get a fair amount of attention)
    Anyway cites are far from being the whole story and it's probably to early to tell anything, certainly to guess at the longterm impact.

    Your excerpt refers to Jacobson's 1995 paper, about GR as "the Einstein equation of state". Great paper! In case anyone is reading this thread who hasn't seen it, I should copy the abstract, too good an opportunity to pass up :oldbiggrin:
    Thermodynamics of Spacetime: The Einstein Equation of State
    Ted Jacobson
    (Submitted on 4 Apr 1995)
    The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation δQ=TdS connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with δQ and T interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravitational lensing by matter energy distorts the causal structure of spacetime in just such a way that the Einstein equation holds. Viewed in this way, the Einstein equation is an equation of state. This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air.
    8 pages, 1 figure.
    Jacobson's paper has 883 cites, evidently the idea that GR is an equation of state of some little "molecules of geometry" intrigued a lot of people. :oldbiggrin:
    Last edited: Dec 28, 2015
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