Okay, here's my train of logic for the meaning of life. It's quite long and rambles at times, but I think that the end result is valid from the starting assumptions. I've broken it down into "Conclusions", "Assumptions", and "Line of Reasoning."
Let me know what you think.
Conclusion: Life is a means of increasing the entropy of the universe. Life is a result of the fact that the equations of dynamics are non-linear, allow for self-replicating structures, and that the starting conditions of the universe are non-equilibrium. The goal of life is to bring the universe to equilibrium at a faster rate than if the equations of dynamics did not allow for life.
Therefore, we as living beings should be trying to increase the entropy of the universe. This means converting as much exergy (such as sunlight) into low grade energy as possible. There are other gradients of exergy that we can take advantage of as well (such as gradients in thermal energy, chemical potential and nuclear potential.) The means to do so are storing "information" (i.e. available electrical/mechanical work) so as to build devices that generate even more entropy. As biologist Stuart Kauffman stated by in "Reinventing the Sacred":
Cells do some combination of mechanical, chemical, electrochemical and other work and work cycles in a web of propagating organization of processes that often link spontaneous and non-spontaneous processes…Given boundary conditions, physicists state the initial conditions, particles , and forces, and solve the equations for the subsequent dynamics—here , the motion of the piston. But in the real universe we can ask, “Where do the constraints themselves come from?” It takes real work to construct the cylinder and the piston, place one inside the other, and then inject the gas…It takes work to constrain the release of energy, which, when released, constitutes work…This is part of what cells do when they propagate organization of process. They have evolved to do work to construct constraints on the release of energy that in turn does further work, including the construction of many things such as microtubules, but also construction of more constraints …Indeed, cells build a richly interwoven web of boundary conditions that further constrains the release of energy so as to build yet more boundary conditions.
There is a balance between using and storing available work (electrical or mechanical). Unfortunately, there is no way to determine what is the optimal balance between storing and using work that will bring the universe to equilibrium at the fastest rate. (i.e. there is no way to predict the fastest route to equilibrium because we can not calculate far enough into the future to determine which route is the fastest to equilibrium.) So, how does life determine which route to take?
It uses neural nets (with some information of past attempts) to estimate which route will bring the system to equilibrium the fastest. But there's no guarantee that it's the best route. Just as there's no guarantee that the answer to the traveling salesman problem is the optimal solution when using neural nets.
Restated: Life is a means of increasing the entropy of the universe and bringing the universe to a state of equilibrium at a faster rate than without life.
Assumptions: 1) Entropy increases due to collisions between particles because the forces of nature are not time reversible. 2) The universe started in a state of non-equilibrium. 3) The future can not be predicted because of the extreme non-linearity of the governing equations. 4) The dynamic equations of systems are highly non-linear and allow for self-replicating structures 5) The self-replicating attractors found in the dynamic equations has a two-fold effect: a) inability to predict the future, and b) ability to store both work and "information" (This self-replicating nature only occurs for systems far-from-equilibrium.)
Line of Reasoning:
Entropy is the number of microstates available to a given macrostate. Entropy defined this way is only valid for large numbers of particles because as N becomes larger (greater than 100,000), then the macrostate with the most microstates ends up being essentially the only macrostate with an probability of occurring. Another way of stating this is asking the question: what is the N-volume of the last dx of an N-D sphere. As N becomes greater than 100,000, then almost all of the volume of the N-D sphere is located at the edge of the N-D sphere.
For the universe, the macrostate is defined by the total energy and total momentum, which are conserved over time.
Assuming that this universe started with a Big Bang (i.e. all of the energy localized in one location), then this represents a state of low entropy. Even though the temperature would have been very high...and I mean almost unimaginably high, the energy would have been confined to a small region of space. There would not have been many microstates available compared with the microstates available today.
There existed a large gradient in energy at the start of the universe, between the location of energy and the rest of the open space in the universe. Diffusion of energy from a region of high energy to low energy would have started immediately.
It can be shown that entropy is defined for both systems in equilibrium and for systems not-in-equilibrium. (See pg 71 eq 6.4 of Grandy's "Entropy and the Time Evolution of Macrosopic Systems.) Since entropy is defined as the number of microstates for the given macrostate with the most microstates, it is a unitless variable. (Note that you can add dimension to entropy by multiplying by k or R. Its unitless definition is convenient because it means that it's relativistically invariant.)
The universe will always be in the given macrostate with the highest entropy because the number of microstates in the given macrostate is so large compared with neighboring macrostates.
The question is then: how does the universe evolve with time? How does it evolve into macrostates with even larger numbers of microstates? When we look around us, we see that there is always an increase in entropy, but most of us have a hard time understanding why.
At the beginning of the universe, the energy was confined to a small region and the probability of finding a "particle" in a certain region or a "field" with a given quanta of energy was larger than it is today. The probability of guessing the actual microstate of the universe near the Big Bang is a lot larger than the probability of guessing the microstate of the universe right now. This loss of information is a loss in the ability to predict the given microstate of the universe. If the number of microstates increases (i.e. entropy increases), then our ability to guess the actual microstate decreases. If we start a confined system in a given microstate, over time we lose information about the actual microstate.
For example, if we start a system with 1,000 particles on left side of a box and then remove the object constraining the particles to the left side of the box. We lose information about the actual microstate as the particles collide. Over time, our ability to predict the given microstate decreases, but at the same time, the symmetry of the system is increasing. Over time, the system will be in the macrostate with the most number microstates. This turns out to be the case in which there is left/right symmetry between the half-way point in the box.
The symmetry of the universe has increased, and then is part of a general trend that "the symmetry of the effect is greater than the symmetry of the cause." (i.e. the Rosen-Curie Principle) (Note that this principle is not violated by nonlinear phenomena, such as Rayleigh-Benard convection cells...it's the total symmetry of the universe that increases because of the increased heat conduction rate.)
The Rosen-Curie Principle is another way of stating the 2nd Law of Thermodynamics, i.e. the number of microstates of the macrostate with the most microstates is increasing with time. [Note: that this means that time can not be reversed. And since there is no symmetry with respect to time reversal, there is no conservation of entropy.]
Note: The idea of increasing symmetry is almost exactly opposite of what's taught to undergraduates in freshman level physics. They are taught that an increas in entropy is equal to an increase in "disorder." This is a incorrect statement and, worse, it's unquantifiable. How do you quantify "disorder" ? You can't. Instead, you can quantify "number of microstates for the macrostate with the larger number of microstates." It's dimensionless and it's relativistically-invariant. You can also quantify the number of symmetries.
So, now that we've seen that entropy increases, we can see where the universe is heading towards. It's heading towards a state of complete symmetry. The final resting state of the universe would be a homogenous state of constant temperature, pressure, chemical potential and nuclear potential. Depending on the size of the universe and questions regarding inflation and proton stability, this could be a state of dispersed iron (which is the state of lowest nuclear Gibbs free energy.) The actual value of the pressure, temperature, and chemical potential depend greatly on whether the universe will continue to just expand into the vastness of space.
If it continues to expand, there may never be a final state of equilibrium, but what we can say is that it will be more symmetric than it is today.
So, going back to the question of life, we have to ask: how does life fit into the picture? Where did life come from and what's the purpose?
Here is my round-about answer to that question. I'm going to address this question by going through the different levels of complexity as one moves from systems in equilibrium to systems far-from-equilibrium. My understanding is that systems far-from-equilibrium are trying to reach equilibrium at the fast possible rate that is allowed by the given constraints in the system.
I see the following levels of complexity:
1) Equilibrium (complete homogeneity) There is symmetry in time and symmetry in space (i.e. the pressure, temperature, electrochemical potential, etc. are constants and not varying with space or time)
2) Linear Non-equilibrium (Gradient in temperature, pressure, electrochemical potential, etc.) But the gradient is small so that the non-linear equation become linear. This is best seen with Ohm's law, in which the directed velocity of electrons due to the gradient of electrical potential is small compared to their thermal speed.
3) Non-linear Non-equilibrium of degree one: The non-linear equations allow for structures to appear that are time independent or time dependent structures that are space-independent. (Such as time independent Ralyeigh-Benard convection cells) This requires a non-linear term in the dynamical equations of the system.
4) Non-linear Non-equilibrium of degree two: The non-linear equations allow for structures to appear that are time dependent. (Such as time dependent Ralyeigh-Benard convection cells) This requires that the system be even further from equilibrium and for non-linear terms.
5) Non-linear Non-equilibrium of degree three/four: Chaotic motion of the system (This also requires a gradient in a potential and it requires that there be a term of cubic power in the equations of motion.) (An example would be a Ralyeigh-Benard cell driven with an extreme temperature gradient such that the cells fluctuate chaotically, i.e. a broad spectrum of frequencies) (We'll use degree three to represent structures with one positive eigenvalue and degree four to represent systems with multiple positive eigenvalues.)
6) Non-linear Non-equilibrium of degree five: Self-referential equations of motion for the system. For systems far-from-equilibrium, there is the possibility that equations can refer back to themselves. These are structures that are formed that can replicate. These structures require a source of exergy (such as a gradient in pressure, chemical potential, etc...) to replicate, but they don't immediately disappear when the source of exergy is turned off. This is due to the fact that exergy is stored within the structure itself. (By exergy, I mean the available work in moving a non-equilibrium system to equilibrium with its environment.) If there is no new source of exergy, then the structure will eventually stop moving and will eventually disappear, like a Ralyeigh-Benard cell disappears after the temperature gradient is removed. At equilibrium, all such structures will disappear.
These structures are capable of storing "information" (i.e. storing gradients in exergy that can be used to generate work), which can be used to generate more "information." "Information return on information investment" Though, the final goal is not more information...the final goal is equilibrium. The "information" is used to speed up the process of reaching equilibrium.
Summary:Equilibrium: no eigenvalues (i.e. no stable structures)
Linear-Non-Equilibrium: negative eigenvalues (i.e. no stable structures, such as convection cells)
Non-linear Non-Equilibrium of order one and two: complex negative eigenvalues (convection cells can form)
Non-linear Non-Equilibrium of order three: one positive eigenvalue (strange attractor has a combination of positive and negative eigenvalues.) (time-varying structures can form)
Non-linear Non-Equilibrium of order four: at least two positive eigenvalues (complex, time-varying structures can form)
Non-linear Non-Equilibrium of order five: the structure is not solvable, i.e. the group describing the eigenvalues is at least as complicated as the group A5 (which is the first nonabelian simple group.)(i.e. Living structures can appear when you are this far way from equilibrium.) The structure is more complicated than the "structure" of a Rayleigh-Benard cell because it has a level of self-reference that allows for replication. The group A5 is the most basic of the building block for order higher groups. One could say that life is about the building of nonabelian, simple structures that survive off a gradient in exergy in order to increase the rate at which the universe reaches equilibrium. (at which point, the structures disappear.)
When the equations of motion allow for "attractors" (i.e. dissipative structures) with symmetries that form a nonabealian, simple group, the structure is capable of replicating. For some higher level of symmetry, there must be the ability for the structure to store information, and it's unclear to me right now what level of group theory is required to allow for storage of exergy. What is clear is that some structures can store "available work" for later use.
The stored "available chemical or mechanical work" is used to overcome the activation energy of chemical reactions. At any given moment in time, the entropy of the universe must increase, so the storage of "available work" must itself generate enough entropy so that at no point in time does the entropy of the universe decrease. With life, we can see that at each step in converting sunlight into stored chemical energy (such as using sunlight to convert ADP to ATP, which can then be used to generate complex carbohydrates), the entropy of the universe increases. There is then a large increase entropy when the complex carbohydrates are oxidized. In that process of oxidation, a large amount of work can be generated. It can either be used to storage more "work" (such as moving against a gravitational field) or can be used to move to a location of a larger gradient in chemical exergy.
There is a balance between using and storing work (electrical or mechanical). Unfortunately, there is no way to determine what is the optimal balance between storing and using work that will bring the universe to equilibrium at the fastest rate. This is due to the fact that there is no way to predict the fastest route to equilibrium because we can not calculate far enough into the future to determine which route is the fastest to equilibrium. So, how does life determine which route to take?
For basic life forms, they always follow the location of the largest gradient in chemical exergy. For more advanced life forms, there are neural nets that store information about the past to predict the future. The predictions are not correct, but over time, the structures build larger and larger neutral nets to better predict the future. Since there is no way to predict the future, there is no right answer. But it appears that the best answer is to generate the largest rate of return on work invested (and note that this is doesn't always mean the fastest replicating structure.) Over time, though, we can see that there is a general trend towards more self-reference, and larger neural networks to predict the future. This involves greater storage of exergy to unleash even more available work. But as I said before, there is no right answer. There is no optimization of the fastest route to equilibrium, so bigger, more complex structures may not necessarily be the best route to increase the entropy of the universe. Though, one clear way to increase the entropy of the universe is to deverlop self-replicating solar robots on other planets so as to increase the entropy of the entire universe.
Restated: life is a means of increasing the entropy of the universe and bringing it to a state of equilibrium at a faster rate than without life. Life only occurs when there is a source of exergy (such as gradients in temperature, pressure or chemical potential with respect to the environment) and when the dynamical equations allow for dissipative structures (i.e. attractors) with symmetries at least as complex as A5 (the first nonabelian, simple group.)