# Can we really apply the second law to the entire universe?

I do not doubt the second law in general, just if it rigorously applied to the entire universe. Here's why I ask this

1. 2nd law - restricted to isolated systems: "The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease" https://en.wikipedia.org/wiki/Second_law_of_thermodynamics

2. Fluctuation theorem - restricted to finite systems: "...for a finite non-equilibrium system in a finite time, the FT gives a precise mathematical expression for the probability that entropy will flow in a direction opposite to that dictated by the second law of thermodynamics"

"...the FT does not state that the second law of thermodynamics is wrong or invalid. The second law of thermodynamics is a statement about macroscopic systems. The FT is more general. It can be applied to both microscopic and macroscopic systems. When applied to macroscopic systems, the FT is equivalent to the Second Law of Thermodynamics" https://en.wikipedia.org/wiki/Fluctuation_theorem

3. Irreversible processes - only in finite time: "In reality, however, truly reversible processes never happen (or will take an infinitely long time to happen)" https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Thermodynamics/The_Four_Laws_of_Thermodynamics/Second_Law_of_Thermodynamics

Doesn't the whole universe violate all 3 of these conditions? It is not isolated, not finite spatially, and infinite in the future. And even for the observable universe, isn't it infinite in the future? This at least violates #3, and I would think #2 as it will be spatially infinite in infinite time.

Can you at least answer how the observable universe isn't infinite in the future to satisfy #2 (i.e. it will keep expanding and thus be infinite spatially) and #3?

• > It is not isolated, not finite spatially, and infinite in the future. Where do these claims come from? I'd say we do not know, we only observe a small part of universe and we do not know future with certainty. – Ján Lalinský Feb 14 at 19:43
• Since it's actually just a statistical observation, I imagine it would be much more apt to vary locally than, say, the gravitational constant (which would leave it easier to understand, &, consequently, more widely-used in cosmology), but I'm not staking my reputation on it. Unfortunately, its wide use may leave it less reliable, while creating an inappropriate impression of probability. – Edouard Feb 15 at 22:19
• @JánLalinský Fair, we do not know those. But then why are physicists so certain the 2nd law will never be violated for the whole universe when the FT (a generalization of the 2nd law) requires finite systems, there is a question whether energy is balanced for entire universe (calls into question requirement of being called isolated), etc, etc. These are questions that need to be answered first no? – J Kusin Feb 15 at 23:06
• @JKusin which physicists? I don't think these are universally accepted beliefs among all physicists. Some may use those as starting assumptions and work out consequences for some specific toy model of universe, but claiming the assumptions hold for out universe is entirely different thing. – Ján Lalinský Feb 15 at 23:21
• @JánLalinský quotes like "The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations — then so much the worse for Maxwell's equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation." - Eddington – J Kusin Feb 16 at 15:55

Imagine for a second that the "thermodynamic universe" is infinite in extent, and it has infinite mass hence infinite internal energy and infinite entropy. What would then the statement mean that in any process the total entropy of the universe that is already infinite can only increase while the infinite total internal energy does not change? What could such statements mean operationally? How could those be tested even in principle?

Despite Clausius's high faluting pronouncement regarding "the" universe to be operationally meaningful the meaning of the "universe" must be restricted from cosmic to galactic/solar/geological scales...

In practice, we examine a system with its immediate neighborhood and just call that to be "universe" but we go even one crucial step further, and introduce idealized work sources along with the concept of an idealized entropy (heat) source/sink.

The crucial idealization is in the assumption that each work source provides a constant mechanical/electrical/magnetic/etc coupling with the system characterized by a single intensive quantity (pressure, stress, E, H, etc.) irrespective of the amount of extensive quantities (volume, strain, charge, polarization, etc.) it has exchanged with the system.

Similarly there is a heat-bath (thermostat) coupled to the system such that the bath's temperature does not change irrespective of the amount of entropy (ie. $$\Delta U_{bath}= T_{bath}\Delta S_{bath}$$ it has exchanged with the system at that temperature (where $$\Delta S_{bath}$$ changes with the interaction while $$T_{bath}$$ stays constant). (Of course, there could be several heat-baths of different temperatures or work sources with different pressures attached and coupled simultaneously to the system so that the system cannot equilibrate but may be in a stable steady state.)

This is reminiscent of the way EEs idealize a battery or any voltage source whose terminal voltage does not change irrespective of its load current. There is no such battery but every electric circuit is designed with that assumption despite the fact that battery voltage depends on its drain. We know so but overcome it with appropriate design so that circuit's range of acceptable performance is maintained. One may say that in the context of Kirchhoff's equations the idealized voltage or current sources (e.g., battery or ac generator, etc.) are the environment of the circuit.

When we specify the bias voltage, or the heat bath temperature, or the the atmospheric pressure as the environment of the system we are giving it boundary conditions, and the system with its boundary conditions is what we call thermodynamic universe without any "cosmic" meaning being attached to it.

1. Is the universe influenced by other universes or a "higher" order of reality? I sure as hell don't know that. If you do I would love for you to support this claim. As far as I know the universe may well be an isolated bubble and I've seen no credible evidence contrary to that assumption.

2. The universe is not in equilibrium because it is in a constant state of change, otherwise nothing would be happening. Once again your question hinges on an unknown assumption. That is 'The universe is infinite in size and therefore also infinite in energy'.

3. For the sake of calculation you can simply restrict yourself to the evolution of the universe between to arbitrary points in time thus making it finite. Your contention only holds if you insist on an infinite time horizon.

• For #1 I've never heard the term 'isolated' used for the whole universe though. #2 Isn't the whole universe assumed infinite for both by most cosmologists? The FT says it only applies to finite systems. #3 How can I justify that exactly. The other laws of physics don't break at infinite times. – J Kusin Feb 14 at 18:37
• #1 This should answer your question physics.stackexchange.com/questions/11701/… #2 No, this is an unsettled issue. #3 Imagine constant acceleration and extend it to infinite future. Are we moving infinitely fast? Any law that describes change over time breaks down eventually. – CookieNinja Feb 14 at 18:49
• I buy their arguments that we can call the universe isolated but then I read "An isolated system obeys the conservation law that its total energy–mass stays constant." en.wikipedia.org/wiki/Isolated_system Is wiki just wrong? Dark energy adds energy. And there is already an infinity in any finite continuum, like empty space. How can we so confidently apply the FT/2nd law when we assume some kind of infinity of the continuum and most treat the universe as infinite spatially even if not settled. The FT says finite only! – J Kusin Feb 14 at 22:41
• "Dark energy adds energy." - Once again you are making assertions about the unknown. How do you know that it "adds energy" and not just releasing energy like a coiled up spring? Here is the thing, based on observation the universe as a whole appear to be increasing in entropy and there is no evidence to the contrary. Any contention is always built on "what if?" and various assumptions backed by no data what so ever. "The universe is infinite." How do you know that? "Dark energy increases energy." How do you know that? "Energy gets made in a vacuum" How do you know that? – CookieNinja Feb 14 at 23:08
• Here's my dilemma. There are well-known physicists saying (paraphrasing) if there is one thing they are sure of, it is the 2nd law (of the univ. ) wont be violated, ever. How can that statement be so strong when we, as you say, don't know if the universe is infinite or not? A lot of theories say it is infinite in some way (contintuum of space, future in time, spatially). And maybe the energy of the univ. is growing. Maybe. So with all these, at the very least, unknowns, how can that view be so self-sure? I rarely see statements that sure/strong in physics or that encompassing (whole univ). – J Kusin Feb 14 at 23:38