Tuesday, March 29, 2016

Entropy: photons, gravity field, black hole entropy, life, universe, economics (Quora answer)

It is often said by experts that the entropy of the universe is not a well defined concept, so it's hard to discuss and is speculative (see Wikipedia "heat death of universe").  But I have included uncontested references as support of most the following statements.

The basis of all standard models of the universe that begin with a big bang is that the entropy of the universe is constant per large-scale expanding volume of the universe . See Stephen Weinberg's 1973ish popular book "The First Three Minutes" where he says this entropy constant is more fundamental than the energy+mass constant of the expanding volume.  Entropy is thereby said to be conserved on a "comoving" volume basis.    This means the average entropy of very large fixed volumes of the universe (where you do not let the meters expand with time due to Hubble's constant) is decreasing. Entropy in "empty" space per fixed volume is decreasing. Gravitational systems where mass is concentrated (like solar systems, black holes, and galaxies) are always emitting and thereby lowering their local entropy (I think of this emitted entropy as "allowing" the universe to expand).
"Entropy always increases" only applies to isolated systems that do not let energy or mass to be exchanged with the surrounding environment. But there is no such thing as an ideally isolated system in nature (see Wikipedia on "isolated system"). "Entropy always increases" is not an exact statement of the second law (reference: search "Feynman entropy"). The exact statement is "W=Q1-Q2" where W is the maximum work that can be extracted from heat reservoirs at T1 and T2 delivering heat Q1 and Q2 which are at different temperatures. For an isolated system  that includes the reservoirs, 0=Q1-Q2-W. But any fixed walls surrounding it will have a temperature that will emit radiation (heat) energy and thereby lower their entropy.  An isolated system with mass inside may have a lower-than universal average entropy and may internally increase in entropy as well as release entropy. Gravity therefore must cause a decrease in local fixed-volume entropy as mass concentrates, and mass concentrating is a direct lowering of entropy. But not only is the mass coming together, but the space-time 4D volume is decreasing from a gravitational effect, further reducing entropy compared to outside meter and time sticks. The number of x*(m*v) states decreases as x decreases, increases as mass increases, and the m/s of v cancels, so gravity space-time warping does not change entropy. I am thinking of the atoms only in terms of a gaseous entropy since the solid state is more complicated, and prior to complete black hole collapse, but these assumptions should lead towards the limits in the right direction.

Why is the entropy of a black hole begin with the same quantity as the entropy of the star that collapses? (As I think is the common view.) Particles closer together is less entropy and I just showed the gravity field change does not have an effect.  Imagine 2 types of particles of a monoatomic gas (no rotational energy to keep things simple), one with positive charge and the other with negative, and they begin as randomly distributed.  As time goes on, let's say they attract and stick, creating a solid which has about 1/10 as much entropy.  Apparently, a potential energy gradient decreasing with distance causing an attractive force is negative entropy (since entropy is conserved). -d(P.E.) = tdS.  This agrees with the two equations I have for force: F=ma= -1*d(PE) and F=+TdS.  The energy in a gravity field decreases as particles come together, which apparently is a direct cause to increase entropy (potential energy is converted to entropy without causing heat). This causes any view of the gravitational field affecting entropy by supposedly affecting space-time to be very problematic since charges are not doing the same.

The Earth's surface  is an open system receiving Sunlight energy, frictional heat energy from the moon's gravity forces, and nuclear decay energy from the core, while releasing a lot of entropy to the universe in the form of photons. Earth's surface might be increasing, decreasing, or constant in its entropy (I can't find an answer and delve into the effect of life in the next paragraph). A geologically dead planet receiving sunlight has a constant amount of entropy, but it is increasing the universe's entropy by turning directed high-energy sunlight photons into a much larger number of undirected low energy photons by being heated up by the Sun. A photon of lower energy has the same amount of entropy as a high energy photon because its lower momentum is offset by it being in a larger region of space (# of states=x*p). So the undirected and larger number are what makes the re-radiated photons (of equal total energy to the incoming photons) have more entropy. See Wikipedia "photon gas" where S=4/3*U/T and since T is randomly directed kinetic energy per particle (see "ideal gas" temperature derivation) and U is total energy, the entropy of randomly directed photons is proportional to their number and inversely proportional to their degree of randomization and not individual energy.

Life is the result of an influx of Gibbs free energy from the Sun, moon, core, and pre-existing geology which produces spontaneous chemical reactions . "Genes" have no physical force in and of themselves, but are durable physical-matter catalysts that are the result of the past dynamics of the available matter under the physical-force influence of the pre-existing and continuing influx of Gibbs free energy. Genes have a continuing effect on the remaining non-gene matter because of the continuing influx of Gibbs free energy.  "Life creates" (more correctly: Gibb's free energy produces) solid structures which have lower entropy but it also emits gases (such as O2 can CO2) that have high entropy which approximately cancel the effect (according to my summing of the specific entropy (entropy/mole) of the products and reactants).   But the products of these reactions that we call life and find useful in economics are the parts that have lower entropy per mass compared to the original ores or gases that we used as inputs.

Structures under higher and higher economic (thinking, cooperative) control have lower and lower entropy because having lower entropy means they are increasingly in "known" states which allows more control giving rise to steel, motors, solar cells, carbon fiber, nanotubes, and computer chips, in concert with pre-existing DNA crystals, bones, shells, and teeth. Stronger bonds almost always means lower entropy because the atoms can't jiggle as far away to different states (states ~ momentum times position=x*p). Entropy per mole of a material = a*ln(x*p)+b where a and b are constants for a given phase (gas, liquid, solid) of a given set of molecules or atoms. x*p depends on volume and temperature, and "a" and "b" depend on mass per particle, ratio of internal energy to temperature (random kinetic energy) of each molecule or atom, and the degree of dependency of the x*p states of each molecule or atom on each other (see "phonons").