Thermodynamics of the Gravity from Entropy Theory

Abstract

The Gravity From Entropy (GfE) action posits that gravity is fundamentally given by the information encoded in the interplay between matter and geometry. The GfE Lagrangian is given by the Geometric Quantum Relative Entropy (GQRE) between the physical metric and the metric induced by matter and curvature, leading to modified gravitational field equations with an emergent dynamical effective dark energy term, which reduce to Einstein’s equations in the low-energy, small-curvature limit. Adopting a thermodynamic viewpoint, we identify the GfE energy density with this emergent effective dark energy term. For homogeneous and isotropic Friedmann-Robertson-Walker spacetimes, we show that GfE universes admit a thermal description: locally, they are characterized by 𝑘-temperatures and 𝑘-pressures satisfying a first law of GfE thermodynamics. In the low-energy, small-curvature regime with perfect-fluid matter and radiation, GfE solutions are well approximated by Friedmann cosmologies. While the total GQRE per unit volume does not increase, the total entropy of GfE universes is nondecreasing in time. We show that, while the total GQRE per unit volume does not increase, consistent with its nature as a relative entropy, the total entropy of GfE universes is nondecreasing in time. These results provide a thermodynamic interpretation of GfE cosmologies and of general relativity itself, recovered in the low-energy, small-curvature limit of the theory, offering a framework to reconcile local order and complexity with the global increase of entropy in the Universe.

Deep dive into the possible persistence of significant cosmological structure deep into the far future of the universe.

Edited Saturday at 09:31 PM1 day by sethoflagos

Entropy from gravitational theory ( specifically thermodynamics related to Black Holes )

Bekenstein-Hawking entropy - Scholarpedia

It goes further than all that - quite recently, Dorau and Much managed to derive the full semi-classical Einstein equations from just relative entropy:

https://doi.org/10.1103/lmq8-nsty

If this result holds - and I’m fairly sure it will -, it will mean that gravity is not a fundamental interaction, but an emergent phenomenon.

I find it hard to believe that classical Einstein equations could be derived from 'quantum relative entropy and its proportionality to an area variation'.
I haven't read the paper ( if I could make heads or tails out of it ), but how do they manage the quantum-classical mix ?

3 hours ago, MigL said:

I find it hard to believe that classical Einstein equations could be derived from 'quantum relative entropy and its proportionality to an area variation'.
I haven't read the paper ( if I could make heads or tails out of it ), but how do they manage the quantum-classical mix ?

The derivation obtains the semi-classical Einstein equations. The term "semi-classical" in this context means that matter fields (more generally: energy-momentum) are treated quantum mechanically, while the geometry of spacetime remains classical. Basically, they start with quantum fields, and show how classical spacetime curvature follows from them via the notion of relative entropy, plus some technical assumptions. They don't quantize spacetime geometry itself. The bridge between the two is given by the Bekenstein-Hawking entropy law, which is assumed in the derivation.

That latter point is where I am somewhat confused though - the Bekenstein-Hawking law is itself a semi-classical result of QFT and GR, so pre-assuming it basically guarantees that you get from QFT to the Einstein equations. Thus, while an important technical result, the whole thing seems just a little bit like a tautology to me. But then again, maybe I am missing something, which is quite possible since QFT isn't my area of expertise.

But my main point stands regardless - the very fact that one can associate thermodynamic entropy with certain types of horizons, while remaining fully consistent with both GR and QFT, indicates to me that gravity is quite possibly not a fundamental thing, but an emergent phenomenon, and this paper strengthens that position. Also, BH horizons having entropy at all seems to imply that the spacetime in the region enclosed by the horizon needs to have some sort of structure or microstates, and can't be smooth and trivial everywhere, or else the very notion of "entropy" associated with them wouldn't make sense.

Just my two cents.

PS. It is worth mentioning that the "relative entropy" referred to here is not standard classical thermodynamic entropy. It is something called Araki-Uhlmann relative entropy, and if I understand this concept correctly (I may not), it essentially measures how different an excited state of a quantum field is relative to the field's vacuum state.

Edited yesterday at 08:24 AM1 day by Markus Hanke

Thank you Markus for bringing this paper to our attention.

It must have taken several years to work all this out, so it will take that much again to work through it with the thoroughness it seems to merit.

Bianconi seems to have presented his working properly, with well defined mostly conventional symbolism, that makes things so much easier for the reader.

However I am always suspicious of circular arguments when I see this sort of thing.

The attempt to constrain the premises to, IMHO, too few variables.

We recently had a couple of long threads involving this.

Edited yesterday at 11:12 AM1 day by studiot

6 hours ago, Markus Hanke said:

The derivation obtains the semi-classical Einstein equations. The term "semi-classical" in this context means that matter fields (more generally: energy-momentum) are treated quantum mechanically, while the geometry of spacetime remains classical. Basically, they start with quantum fields, and show how classical spacetime curvature follows from them via the notion of relative entropy, plus some technical assumptions. They don't quantize spacetime geometry itself. The bridge between the two is given by the Bekenstein-Hawking entropy law, which is assumed in the derivation.

That latter point is where I am somewhat confused though - the Bekenstein-Hawking law is itself a semi-classical result of QFT and GR, so pre-assuming it basically guarantees that you get from QFT to the Einstein equations. Thus, while an important technical result, the whole thing seems just a little bit like a tautology to me. But then again, maybe I am missing something, which is quite possible since QFT isn't my area of expertise.

But my main point stands regardless - the very fact that one can associate thermodynamic entropy with certain types of horizons, while remaining fully consistent with both GR and QFT, indicates to me that gravity is quite possibly not a fundamental thing, but an emergent phenomenon, and this paper strengthens that position. Also, BH horizons having entropy at all seems to imply that the spacetime in the region enclosed by the horizon needs to have some sort of structure or microstates, and can't be smooth and trivial everywhere, or else the very notion of "entropy" associated with them wouldn't make sense.

Just my two cents.

PS. It is worth mentioning that the "relative entropy" referred to here is not standard classical thermodynamic entropy. It is something called Araki-Uhlmann relative entropy, and if I understand this concept correctly (I may not), it essentially measures how different an excited state of a quantum field is relative to the field's vacuum state.

This is all well beyond my grasp of physics but if gravitation were an emergent phenomenon rather than a fundamental interaction, would that get rid of the intractable problems associated with the (so far hypothetical) graviton? I can imagine that in that case one might no longer need to try to treat gravitation in terms of QFT, with its own mediating particle and so forth.

Thanks Markus.
Interesting(?) that, since Bekenstein-Hawking Entropy is assumed, we had to expect the obtained result.
Somewhat circular, but I, and Exchemist, are puzzled as to why this indicates gravity may be emergent.
Or am I misunderstanding you ?

Edited 19 hours ago19 hr by MigL

3 hours ago, MigL said:

Thanks Markus.
Interesting(?) that, since Bekenstein-Hawking Entropy is assumed, we had to expect the obtained result.
Somewhat circular, but I, and Exchemist, are puzzled as to why this indicates gravity may be emergent.
Or am I misunderstanding you ?

Actually I’m not puzzled by that so much. I was just wondering whether emergent gravitation might do away with some of the intractable problems people seem to have had developing a quantum theory of gravity.

9 hours ago, MigL said:

Somewhat circular, but I, and Exchemist, are puzzled as to why this indicates gravity may be emergent.

In the same sense that eg the Navier-Stokes equations are “emergent” from the statistics of particulate fluids and gases.

The broader picture here is that, every time you start with QFT in general spacetimes with as-yet unconstrained metric, and add in the concepts of relative entropy plus some more technical tools (modular theory), the Einstein equations arise as consistency conditions. This is the same as, when you start with general particle ensembles and add in Newtonian forces and conservation principles, the emergent global “statistics” of these fluids are shown to obey Navier-Stokes. It that sense, NS is emergent. Same with gravity - the interplay of quantum fields and their relative entropies is consistent if and only if the background spacetime has a particular geometry that fits the configuration of quantum fields in question.

12 hours ago, exchemist said:

I can imagine that in that case one might no longer need to try to treat gravitation in terms of QFT, with its own mediating particle and so forth.

Exactly.

NB. The consistency conditions always turn out to be ordinary Einsteinian GR, not any of the many proposed alternatives or modifications.

Edited 9 hours ago9 hr by Markus Hanke

You guys might like to explore this website, which is also the website associated with the book I reviewed in the lounge.

Emergence is a particular topic

The Material World - Physics Fixes All the Facts

Complex systems seem to magically emerge from the interactions of their parts. A whirlpool emerges from water molecules. A living cell from organic molecules. You emerge from the cells of your body

Markus mentions Navier Stokes.

A word of caution here.

In the 19th cent Messers Navier and Stokes constructed their equation to include all known contributory variables, which is why it is so difficult to solve.

In the 20th cent Messers Black and Scholes thought they would do the same with economic systems.

Unfortunately they did not do such a thorough job, which is why computer implementations of their equation caused the instability and stock market crash of 2008.

We should beware of what we wish for when declaring emergence, we might well find something quite different from what we expect.

Edited 3 hours ago3 hr by studiot

44 minutes ago, studiot said:

We should beware of what we wish for when declaring emergence, we might well find something quite different from what we expect.

Yes, very valid point +1

I did not mean to make the thread above sound like the last words have been spoken on these matters...it's just that the connection between gravity and thermodynamics seems to be too strong to be a mere coincidence. And thermodynamics is "emergent" in the sense that it is a statistical macroscopic description of systems made up of microscopic constituents (or states).