Here are some silly quotes I've seen over the last day:

"We should applaud the continued progress, and that entrepreneurs iterate as superior technology becomes available. This is how innovation happens, but the [Wall Street] Journal does not really understand innovation."

&

"The bigotry of 'government' shouldn't do anything.'"

From The Wall Street Journal Op-ed, Vinod Kholsa 2/22/2011

So, Vinod Kholsa is starting to sound like one of those Middle Eastern dictators.

Defending the regime up until the very end. Calling people 'bigots' who don't want the government to support wasteful spending. Whoah! This is a new low for a CEO. Calling people bigots who don't want him to get rich!

I hope that the Republicans in Congress start looking into Waste, Fraud & Abuse within the companies supported by the DOE/NREL to see if Vinod ended up making money at the expense of tax payers.

Perhaps, Vinod may well end up in jail like the Enron executives who used political clout to steal millions in dollars.

And here's the (ironically) best quote from the Range Fuels CEO, .

"When gasoline hits $4.50 per gallon, let's chat again."

Wall Street Journal Op-ed, David Aldous 2/22/2011

This is what I was saying in my previous comment. When gasoline hits $4.50 a gallon, cellulosic ethanol will still not be competitive with gasoline. (Because their capital/fuel/labor costs will all be higher now that all energy is more expensive if gasoline reaches $4.50.) What we need to do is to calculate a total average rate of return on investment. (This will be part of my next blog.)

I wish that there was an easier why to tell hype, from from people like Vinod Kholsa and David Aldous, from truth in the energy business. We all need to stop believing the hype from CEOs like Vinod Kholsa and David Aldous. We need a people's revolt against people like them who get rich through their political connections. I hope that we all learn how to "Curb your Enthusiasm" and conduct some due diligence.

Due diligence: How to evaluate an energy technology

And here's the last of the quotes

"Spending about 2% of global GDP in 10 key areas would kick-start a 'low carbon, resource efficient green economy' "

UN "Green Economy" programme

Grow by not Growing

Spending 2% of global GDP on people like Vinod Kholsa and David Aldous will not kick start a low carbon, resource efficient green economy. You can't grow by not growing! You notice how the amount is just enough to get some people rich, but not enough to actually get us pissed off enough to protest against the wasteful spending?

This UN report also recommended following policies that decoupled economic growth from intensive consumption.

Here's the problem with the UN's thinking : Economic growth means intensive consumption.

Building wind turbines, solar cells, ethanol plants, etc. is extremely resource intensive. So is building nuclear or coal power plants.

In order to grow (which is what life does), we have to realize that we will be having an impact on the Earth. But not only Earth, we also need to be making an impact on other planets. There is no growth if we're stuck on this planet. Growth means consuming more and more, on more and more planets.

So, send me some more silly quotes from people who think they 'know' how solve the energy crisis if we just give them some more money!

## Tuesday, February 22, 2011

## Thursday, February 17, 2011

### Maintaining a Sense of Humility

I want to make sure that readers of this blog understand that the laws of physics do not tell us anything about what type of political or economic systems to support.

There is nothing in the First or Second Law of Thermodynamics that supports one type of political party over another. There is nothing in the principle of "Maximize the Rate of Return on Investment in order to Maximize the Entropy Production Rate" that should lead a person to support one economic theory over another.

Even though it may sound like Maximizing the Rate of Return on Investment is pro-capitalism, there is nothing in that principle that states that, therefore, we must all be capitalists. As I mentioned in a previous blog, there is no way to prove which route will lead to the maximization of entropy. i.e. there is no guaranteed way to prove that your way of maximizing entropy is actually the best way.

Disproving a Maximum Or Minimum Rate of Entropy Production

Since there is no way to prove that your way of doing things is better at maximizing entropy production than somebody else's way of doing things, then we have to treat other people with respect because we never know if their way of living is better than our way of living.

We have to respect the views of all people: including capitalists, socialists, communist and other. For example, there is no way to prove that one's calculation of the Rate of Return on Investment for Process A will actually come true, and this is due to the fact that the future is uncertain. Not just for humans, but for all life forms, even supercomputers.

But just because we respect other people's views, doesn't mean that we should believe in their views. We should still calculate the Rate of Return on Investment of various processes and then chose the one with the largest calculated rate of return on investment. We should, though, always keep in mind that there's no way to prove mathematically that one's choice is actually the best choice to make, and because of this uncertainty, we should always maintain a certain sense of humility. People with different views are not our enemy. We should want other people to figure out for themselves how to maximize the rate of return on investment of their own money, knowing that this is best for everybody.

The reason that the principle of "Maximize the Rate of Return on Investment in order to Maximize the Entropy Production Rate" does not support capitalism over socialism is also the fact that we do not know what the optimal route is to maximize the rate of entropy production.

Perhaps, if everybody was guaranteed a job and healthcare, then people on average would become more productive. But perhaps guaranteeing a job and healthcare would cause people to get lazy. There's no way to prove that guaranteeing a job and healthcare is better or is worse than not guaranteeing a job and healthcare. And there's no economic model that can prove either way. As well, there's no real world proof either because there's no way to try both economic theories out at the same time and same place in order to compare them on an equal footing. And even if we could test the alternatives at the same time and same place, there's no way to prove that just because something worked better at one point in time, that it will work better than another option at some point in time in the future. For example, there was no way to predict 20 years ago that the societies with the largest rate of returns on investment (China and India) would be countries that are neither capitalist or socialist. Both are some combination of capitalism and socialism.

So, this leads me back to the main point I want to make: the laws of physics suggest that we need to maintain a sense of humility. Why? Because there is no way to prove how to maximize the quantity that life is trying to maximize (entropy production rate).

The uncertainty of the future mean that we need to respect people of differing belief systems (political, economic & religious.)

There is nothing in the First or Second Law of Thermodynamics that supports one type of political party over another. There is nothing in the principle of "Maximize the Rate of Return on Investment in order to Maximize the Entropy Production Rate" that should lead a person to support one economic theory over another.

Even though it may sound like Maximizing the Rate of Return on Investment is pro-capitalism, there is nothing in that principle that states that, therefore, we must all be capitalists. As I mentioned in a previous blog, there is no way to prove which route will lead to the maximization of entropy. i.e. there is no guaranteed way to prove that your way of maximizing entropy is actually the best way.

Disproving a Maximum Or Minimum Rate of Entropy Production

Since there is no way to prove that your way of doing things is better at maximizing entropy production than somebody else's way of doing things, then we have to treat other people with respect because we never know if their way of living is better than our way of living.

We have to respect the views of all people: including capitalists, socialists, communist and other. For example, there is no way to prove that one's calculation of the Rate of Return on Investment for Process A will actually come true, and this is due to the fact that the future is uncertain. Not just for humans, but for all life forms, even supercomputers.

But just because we respect other people's views, doesn't mean that we should believe in their views. We should still calculate the Rate of Return on Investment of various processes and then chose the one with the largest calculated rate of return on investment. We should, though, always keep in mind that there's no way to prove mathematically that one's choice is actually the best choice to make, and because of this uncertainty, we should always maintain a certain sense of humility. People with different views are not our enemy. We should want other people to figure out for themselves how to maximize the rate of return on investment of their own money, knowing that this is best for everybody.

The reason that the principle of "Maximize the Rate of Return on Investment in order to Maximize the Entropy Production Rate" does not support capitalism over socialism is also the fact that we do not know what the optimal route is to maximize the rate of entropy production.

Perhaps, if everybody was guaranteed a job and healthcare, then people on average would become more productive. But perhaps guaranteeing a job and healthcare would cause people to get lazy. There's no way to prove that guaranteeing a job and healthcare is better or is worse than not guaranteeing a job and healthcare. And there's no economic model that can prove either way. As well, there's no real world proof either because there's no way to try both economic theories out at the same time and same place in order to compare them on an equal footing. And even if we could test the alternatives at the same time and same place, there's no way to prove that just because something worked better at one point in time, that it will work better than another option at some point in time in the future. For example, there was no way to predict 20 years ago that the societies with the largest rate of returns on investment (China and India) would be countries that are neither capitalist or socialist. Both are some combination of capitalism and socialism.

So, this leads me back to the main point I want to make: the laws of physics suggest that we need to maintain a sense of humility. Why? Because there is no way to prove how to maximize the quantity that life is trying to maximize (entropy production rate).

The uncertainty of the future mean that we need to respect people of differing belief systems (political, economic & religious.)

## Wednesday, February 9, 2011

### On Utillity, Price, and Cost

The goal of this post is to differentiate between utility, price and cost.

There is a philosophy called utilitarianism which states that the goal of human life is to maximize the utility of human life. The problem has been that, since the inception of this philosophy, there has been no way to quantify this term 'utility.' Some people say that utility is pleasure, some say that utility is knowledge, while others say that utility is money.

So, what's the point of a philosophy if we can't even define what we're trying to maximize?

Simply put, there is no point in having a philosophy if we can't define what we're trying to maximize. Though, what's important about utilitarianism is that it gets us thinking about what we are doing here on Earth. What is the goal of life? What is it that we are trying to maximize? Or perhaps instead, are we trying to minimize something, like pain or poverty?

Utilitarianism is a form of consequentialism, which states that the moral worth of an action is determined by its outcome.

So, there are quite a few similarity between utilitarianism and the "philosophy" of maximizing the rate of return on work invested. In both cases, the goal is to maximize a certain quantity. In both cases, the moral worth of an action is determined by its outcome (as opposed to the intention.) In both cases, the quantity being maximized is impossible to calculate accurately. (utility is impossible to calculate because it's ill-defined & rate of return on investment is impossible to calculate because we can't predict the future.)

So, now with this background, I'd like to discuss the difference between utility, price and cost. Sometimes, I'll use the unit of kW-hr instead of $ because we can always assume that we live in a country with an electricity-backed-currency. (Check out the previous post on Electricity Backed Currency for more details.)

Utility is the amount of value for the customer who buys a product. Value can mean a lot of different things to different people. For some people, value can mean pleasure, for some it means spirituality. For other people, the value of a product is equal to its capability to produce a return on investment. For these people, they can try to estimate how much return on investment they would get by buying the product, and from that calculation, they could estimate the maximium amount that they would be willing to pay. For them, utility is the amount that they would pay at which their rate of return is exactly zero.

Similarly, but from the other side, cost is amount of work (kW-hr) required to build the product with zero profit. A company can roughly estimate how expensive it will be to manufacture a product at a given rate (# of products per time). The cost to make the product does not include the profit that the company makes when they sell the product above the cost.

So, this leaves the price of the product. For some people, the utility of the product is larger than the cost of the product, and therefore it's possible for the buyer and seller to find an intermediate price that is beneficial to both people. For others, the utility is less than the cost, and there is no price that is mutually beneficial. (check out the previous post on Comparison between Supply & Demand Curves)

In the end, the company will try to maximize their total profits, and they can do that by estimating the cost as a function of the # of products per time as well as the number of people who will buy the products as function of the utility.

Interestingly, both of these functions can be graphed. (One axis has the units of kW-hr... i.e. $, and the other axis is # of products per time.)

The company should graph the two curves, and the location where the two curves meet. At this price, the company can maximize its profits, and the buyers can maximize their eventual return on investment. A win-win for all parties, i.e. the price is the kW-hr ($) for the product that gives the greatest 'return on investment' for the most people. And so we return back to utilitarianism. The price of a product is not the utility and its not the cost. The price is the amount of work (kW-hr) exchanged in order to maximize the greatest good for the greatest number of people.

So, in summary:

utility = the kW-hr of work exchanged such that the customer will obtain a zero rate of return on investment. (Any price below this leads to a positive rate of return on investment for the customer.)

cost = the amount of work (kW-hr) required to build the product with zero profit. (For any price above the cost leads to profit for the company.)

price = the exchange of work (kW-hr / $) that creates the maximize good for the greatest number of people.

There is a philosophy called utilitarianism which states that the goal of human life is to maximize the utility of human life. The problem has been that, since the inception of this philosophy, there has been no way to quantify this term 'utility.' Some people say that utility is pleasure, some say that utility is knowledge, while others say that utility is money.

So, what's the point of a philosophy if we can't even define what we're trying to maximize?

Simply put, there is no point in having a philosophy if we can't define what we're trying to maximize. Though, what's important about utilitarianism is that it gets us thinking about what we are doing here on Earth. What is the goal of life? What is it that we are trying to maximize? Or perhaps instead, are we trying to minimize something, like pain or poverty?

Utilitarianism is a form of consequentialism, which states that the moral worth of an action is determined by its outcome.

So, there are quite a few similarity between utilitarianism and the "philosophy" of maximizing the rate of return on work invested. In both cases, the goal is to maximize a certain quantity. In both cases, the moral worth of an action is determined by its outcome (as opposed to the intention.) In both cases, the quantity being maximized is impossible to calculate accurately. (utility is impossible to calculate because it's ill-defined & rate of return on investment is impossible to calculate because we can't predict the future.)

So, now with this background, I'd like to discuss the difference between utility, price and cost. Sometimes, I'll use the unit of kW-hr instead of $ because we can always assume that we live in a country with an electricity-backed-currency. (Check out the previous post on Electricity Backed Currency for more details.)

Utility is the amount of value for the customer who buys a product. Value can mean a lot of different things to different people. For some people, value can mean pleasure, for some it means spirituality. For other people, the value of a product is equal to its capability to produce a return on investment. For these people, they can try to estimate how much return on investment they would get by buying the product, and from that calculation, they could estimate the maximium amount that they would be willing to pay. For them, utility is the amount that they would pay at which their rate of return is exactly zero.

Similarly, but from the other side, cost is amount of work (kW-hr) required to build the product with zero profit. A company can roughly estimate how expensive it will be to manufacture a product at a given rate (# of products per time). The cost to make the product does not include the profit that the company makes when they sell the product above the cost.

So, this leaves the price of the product. For some people, the utility of the product is larger than the cost of the product, and therefore it's possible for the buyer and seller to find an intermediate price that is beneficial to both people. For others, the utility is less than the cost, and there is no price that is mutually beneficial. (check out the previous post on Comparison between Supply & Demand Curves)

In the end, the company will try to maximize their total profits, and they can do that by estimating the cost as a function of the # of products per time as well as the number of people who will buy the products as function of the utility.

Interestingly, both of these functions can be graphed. (One axis has the units of kW-hr... i.e. $, and the other axis is # of products per time.)

The company should graph the two curves, and the location where the two curves meet. At this price, the company can maximize its profits, and the buyers can maximize their eventual return on investment. A win-win for all parties, i.e. the price is the kW-hr ($) for the product that gives the greatest 'return on investment' for the most people. And so we return back to utilitarianism. The price of a product is not the utility and its not the cost. The price is the amount of work (kW-hr) exchanged in order to maximize the greatest good for the greatest number of people.

So, in summary:

utility = the kW-hr of work exchanged such that the customer will obtain a zero rate of return on investment. (Any price below this leads to a positive rate of return on investment for the customer.)

cost = the amount of work (kW-hr) required to build the product with zero profit. (For any price above the cost leads to profit for the company.)

price = the exchange of work (kW-hr / $) that creates the maximize good for the greatest number of people.

### An awesome video game I'd like to make called "Entropy"

So, I've been wanting to make a video game that's a mix of SimCity and Civilization. The name of the game is "Entropy," and as you can guess, the goal is to generate as much entropy as possible, and be the last civilization standing. So, unlike Sid Meier's Civ games, there'd only be one way to win the game, and that's by producing more entropy than any of the other civilizations.

In the Civilization games, there are multiple ways to win: through battle, through knowledge, through space exploration, or through diplomacy. And in SimCity, there's no real way to win, but you can compete against your friends to see who has the wealthiest city after a given number of turns.

Let me know if anybody has expertise modifying either the SimCity or Civilization games so as add in a counter that could track the production of entropy (where entropy production numbers would assigned for each action, such as movement, building, energy production, etc...)

I'd like to run some experiments to study the best methods for producing entropy at the fastest rate.

As I've mentioned in previous posts, there is no way to prove that a different route will be the fastest route to producing the most entropy.

Disproving a maximum or minimum of Entropy Production Rate

So, I'd like to check whether the figure of merit "average rate of return on work invested" ends up being the best way to increase the rate of entropy production, as I quickly demonstrated in the Thought Experiment for Maximizing the Rate of Entropy Production.

So, let me know if you know of a video game that can be adapted to implement the entropy calculations that I mentioned above.

Also, i've had an idea for a video game where you are a power plant engineer/manager.

Let me know if you have any expertise here, and would like assistance writing the script/plot of the video game (I don't program well at all, so I can't be of assistance here.)

eddie.devere7@gmail.com

In the Civilization games, there are multiple ways to win: through battle, through knowledge, through space exploration, or through diplomacy. And in SimCity, there's no real way to win, but you can compete against your friends to see who has the wealthiest city after a given number of turns.

Let me know if anybody has expertise modifying either the SimCity or Civilization games so as add in a counter that could track the production of entropy (where entropy production numbers would assigned for each action, such as movement, building, energy production, etc...)

I'd like to run some experiments to study the best methods for producing entropy at the fastest rate.

As I've mentioned in previous posts, there is no way to prove that a different route will be the fastest route to producing the most entropy.

Disproving a maximum or minimum of Entropy Production Rate

So, I'd like to check whether the figure of merit "average rate of return on work invested" ends up being the best way to increase the rate of entropy production, as I quickly demonstrated in the Thought Experiment for Maximizing the Rate of Entropy Production.

So, let me know if you know of a video game that can be adapted to implement the entropy calculations that I mentioned above.

Also, i've had an idea for a video game where you are a power plant engineer/manager.

Let me know if you have any expertise here, and would like assistance writing the script/plot of the video game (I don't program well at all, so I can't be of assistance here.)

eddie.devere7@gmail.com

## Tuesday, February 8, 2011

### My real problem energy tech with low rate of return on investment

My real problem with energy technologies that generate low rate of return on investment (such as solar cells today) is that if we were all of a sudden to switch to solar PV, then roughly one in every three people would be required to build solar cells and install them.

The inverse of the total return on investment (which is roughly equal to the RROI times the lifetime) is proportional to the percentage of the population required to build and install a certain technology.

Right now, the rate of return on investment for solar cells is really low, and the 'pay back time' is roughly 10 year. Since the plant lifetime is roughly 30 yrs, the total return on investment is roughly 200%. In this case, the net energy was double the amount of electricity generated as what went into building it.

What is a typical return on investment for solar panels?

So, let's imagine that all of the electricity on the globe was generated from these solar cells (with a ROI of 200%.) So, since the building of solar cells uses 1/3 of the electricity that is generated by the solar cell, then this means that 1/3 of the global population must be devoted to the building of the solar cell. This leaves only two thirds of the population to farm, to be doctors, to be artists, to be educators, etc...

So, the real problem with energy technology with low rates of return on investment is that more and more of us will have to take jobs in the energy field.

As the rate of return on investment decreases for electricity generation or oil/natural drilling, then the profits for the oil/natural gas/coal/electricity companies decrease. Why did profits decrease? Because the companies had to pay more people to do the work of what use to take fewer people. As the companies have to hire more people, the profits for the people at the top and bottom decrease. This means that they have less money to spend on vacations, education, art, etc... This means that there are less people employed in these "non-energy" positions. When these people become unemployed, they drive down salaries because an unemployed person is willing to work for less money than a person who is already employed.

Eventually, the salary of everybody (in real dollars, i.e. taking into account inflation) is less than when the energy rate of return on investment was larger.

So, in the short run, increasing energy prices causes employment, but only in the short term (and that's only because of the irreversibility of looking for employment, such as difficulty moving cities, unwillingness to accept certain jobs/salaries, and the time it takes applying for positions.)

In the long term, what happens is that more and more of the population is employed in the energy field, and less people are employed in non-energy fields. This means less artists, less professors, less dancers, less athletes, etc...

In summary, the problem I have with energy technologies with a low rate of return on investment is that more of us have to be building, installing & maintaining the technology. And this means that there will be less people with free time to engage in the arts. We need to remember this when we say that we are willing to pay more for "clean" electricity. This means that we have less money for the arts.

I'm all for clean electricity if it can compete with the high rate of return investment technology that we'd had for the last century, but if it can't, then we need to seriously weigh alternatives:

Clean energy tech and fewer non-energy workers, i.e. fewer video game developers/hotel clerks/etc...

Dirty energy tech and more non-energy workers.

So, when somebody says, "I'm for clean energy jobs!" Remember that they are also implying, "I'm for less non-energy jobs!"

The inverse of the total return on investment (which is roughly equal to the RROI times the lifetime) is proportional to the percentage of the population required to build and install a certain technology.

Right now, the rate of return on investment for solar cells is really low, and the 'pay back time' is roughly 10 year. Since the plant lifetime is roughly 30 yrs, the total return on investment is roughly 200%. In this case, the net energy was double the amount of electricity generated as what went into building it.

What is a typical return on investment for solar panels?

So, let's imagine that all of the electricity on the globe was generated from these solar cells (with a ROI of 200%.) So, since the building of solar cells uses 1/3 of the electricity that is generated by the solar cell, then this means that 1/3 of the global population must be devoted to the building of the solar cell. This leaves only two thirds of the population to farm, to be doctors, to be artists, to be educators, etc...

So, the real problem with energy technology with low rates of return on investment is that more and more of us will have to take jobs in the energy field.

As the rate of return on investment decreases for electricity generation or oil/natural drilling, then the profits for the oil/natural gas/coal/electricity companies decrease. Why did profits decrease? Because the companies had to pay more people to do the work of what use to take fewer people. As the companies have to hire more people, the profits for the people at the top and bottom decrease. This means that they have less money to spend on vacations, education, art, etc... This means that there are less people employed in these "non-energy" positions. When these people become unemployed, they drive down salaries because an unemployed person is willing to work for less money than a person who is already employed.

Eventually, the salary of everybody (in real dollars, i.e. taking into account inflation) is less than when the energy rate of return on investment was larger.

So, in the short run, increasing energy prices causes employment, but only in the short term (and that's only because of the irreversibility of looking for employment, such as difficulty moving cities, unwillingness to accept certain jobs/salaries, and the time it takes applying for positions.)

In the long term, what happens is that more and more of the population is employed in the energy field, and less people are employed in non-energy fields. This means less artists, less professors, less dancers, less athletes, etc...

In summary, the problem I have with energy technologies with a low rate of return on investment is that more of us have to be building, installing & maintaining the technology. And this means that there will be less people with free time to engage in the arts. We need to remember this when we say that we are willing to pay more for "clean" electricity. This means that we have less money for the arts.

I'm all for clean electricity if it can compete with the high rate of return investment technology that we'd had for the last century, but if it can't, then we need to seriously weigh alternatives:

Clean energy tech and fewer non-energy workers, i.e. fewer video game developers/hotel clerks/etc...

Dirty energy tech and more non-energy workers.

So, when somebody says, "I'm for clean energy jobs!" Remember that they are also implying, "I'm for less non-energy jobs!"

## Wednesday, February 2, 2011

### On Irreversibility

It's been said before, even by some really smart people, that the universe is reversible because the underlying equations of motion are time-reversible.

And while there are plenty of equations in physics that are time-reversible (such as Dirac's, Schrodinger's, and Newton's), there are just as many equations that are time-irreversible (Boltzmann's, Fick's, Ohm's, and Fourier's).

My goal in this post is to walk through the arguments explaining why the universe is irreversible.

While this statement is a no brainer to 99.9% of the world's population, it still doesn't mean it's proven. And because of this, there's still some 0.1% of the population who have fallen in love with the elegance of time-reversible equations (and trust me, even I find Dirac's equation to be extremely beautiful,) and have taken this as 'proof' that the world is reversible.

So, here's my line of reasoning for why the world is irreversible.

Let's take the well-known case of a gas expanding into twice its initial volume after removing a partition. There is a well defined pressure and temperature in the gas, yielding a well-defined entropy, enthalpy, etc... We can say with 100% probability that the gas is not on the other side of the partition. We do not know the exact microstate of the gas any given moment in time, but we can rule out any microstate in which there are gas molecules on the empty side of the partition.

So, to re-emphasize, we don't know the exact microstate of the system, but there are some microstates that we can rule out.

So, what happens when we withdraw the partition? At first, nothing. But slowly, the molecules move about, and start filling the volume. We eventually cannot rule out the microstates that we had ruled out earlier (i.e. those microstates in which particles are in the initially empty half of the container.) Once we remove the partition, we introduce new microstates, but we can't rule out any of the microstates from before either. This means we have increased the number of microstates available to the system. And now, there is no way to go back to the point in time in which less microstates were available, without doing work on the system (which increases the number of available microstates in a neighboring system.) While any of the microstates of the original (with partition) system are available (though with small probability), what we have lost is information about the system. There are more available microstates, hence, our probability of guessing the exact microstate at any given time has decreased. Our information about the system has decreased. And while Poincare's reoccurrence theorem says that a system will eventually return to near its initial conditions, the point is that we cannot predict when this will happen, so either way you think about, we have lost information about the system.This loss of information is the underlying feature of irreversible phenomena, such as diffusion, chemical reactions, and heat transfer. They are irreversible because there is an overall loss of information about the possible microstate of the system.

What's really happening from a microstate point of view?

I'm going to try to explain this using the example of an 6N-dimensional sphere. (Each of the N particles has 3 space coordinates and 3 momentum coordinates. In the example above, the gas is confined to one half of the box before the partition is removed. In 6N-dim space, we can image that each of the microstates, in which the gas can exist, are points in this space. When we say that the system has a defined pressure and temperature, what we are saying is that the gas is most likely to exist in one of the microstates in the outer most sliver of the 6N-dimensional sphere. [Note: the percent volume of the last sliver of a N-dim sphere increases with N such that when N becomes greater than roughly 1000, over 99.9% of the volume of the 6N-dim sphere is in the outer most sliver. This means that the rest of the sphere's volume is extradinarily small, but not zero.]

The macrostate corresponding to the 'pressure' and 'temperature' of the confined gas is the macrostate associated with all of those microstates near the edge of the sphere, but this doesn't rule out the possibility of the system being in one of the states further inside the sphere. What we can rule out is the system being in a microstate outside of the sphere.

This changes when we remove the partition. The gas is diffusing in 6N-dim all the time, but now that the partition is removed, it can expand into a larger space in 6N-dim. This larger space incorporates all of the prior microstates, but adds many more. And when N is the size of Avogadro's number, then the number of new microstates dwarfs the number of old microstates, i.e. the actual microstate of the system is most likely to be one of the microstates at the edge of the new 6N-dim volume, because that's where almost all of the volume is. This doesn't mean that the actually microstate can be one of the prior ones, it's just extremely unlikely.

So, when a system goes from (p0, T0) to (p1, T1), it's diffusing into a larger 6N-dim volume, that incorporates the smaller 6N-dim volume before hand.

This is why Poincare's reoccurrence theorem can be true, but yet the universe can be irreversible. The universe is expanding into a larger 6N-dim volume all the time. And there is no way to confine it to a smaller volume. There's only one direction, and that's the direction of larger 6N-dimensional volume.

So, when we say that the entropy of the universe is increasing, what we mean is that the total number of microstates available in the universe is increasing (i.e. the 6N-dim volume is increasing.) Any (and I mean any) of the prior microstates is still a possible microstate, but with every moment, the probability of being in one of those earlier microstates decreases.

Information about the exact microstate of the universe is decreasing because the total number of microstates is increasing. The irreversibility of the universe is a sign of the underlying diffusion of particles/waves/fields into microstates that were not available in the past.

So, now I want to discuss why there is loss of information, and answer the question of where does the information go?

So, my understanding is that there are two main requirements for the universe to be irreversible.

1) There must be collisions between particles that can interact via the 'time-assymetric' weak nuclear force

2) The universe must have started in a non-equilibrium (i.e. a macrostate with many, many, many less possible microstates than the current or any future macrostate.) [This of course lends itself to the theory of the Big Bang because a universe expanding (diffusing) into a larger volume is consistent with the diffusion we 'see' in 6N-dim space in all irreversible processes.

My understanding of the universe is that energy/mass is conserved for all time (and this probably means energy/mass conservation before the Big Bang as well) and that the number of microstates available to the universe is increasing. Information disappears about which microstate the universe is in and is not in.

Subscribe to:
Posts (Atom)