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Hi,

Owen wrote:

Brendan wrote:

Owen wrote:You can go and do the calculations for it if you want. With perfect computational efficiency, the total energy in the solar system is less than that required to do 2^127 block decryptions.

No I can't. The calculations rely on the false assumption that changing state must consume energy (rather than merely storing energy and reclaiming previously stored energy). All calculations that rely on false assumption are wrong by default.

"The temperature of the cosmic microwave background radiation gives a practical lower limit to the energy consumed to perform computation of approximately 4kT per state change, where T is the temperature of the background (about 3 kelvins), and k is the Boltzmann constant. While a device could be cooled to operate below this temperature, the energy expended by the cooling would offset the benefit of the lower operating temperature."

I can't see what any of this has to do with what I wrote. What I wrote has nothing to do with temperatures at all. For a simple example, imagine a system of iron balls being pushed by electro-magnets made out of superconductors in a perfect vacuum (energy converted from electricity to momentum, and energy converted from momentum to electricity).

Owen wrote:(See Lloyd 1999)

This talks about speed of computation. It has no relevance.

Owen wrote:(Or: You can't break even except at absolute zero, and you can't ever reach absolute zero)

Also assumes temperature is involved in some way.

Owen wrote:

Brendan wrote:

Owen wrote:And the first thing you ignored is that the Carnot engine equations only apply for a heat engine - a device which converts thermal energy to work.

You already stated that CPUs convert 100% of electrical energy into heat energy (I implicitly agree). Converting heat back into some other form of energy (e.g. electricity) is the only part where we disagree, which is what the Carnot engine does.

The Carnot engine converts a difference in temperatures to energy, not heat.

Same end result.

Owen wrote:

Brendan wrote:

Owen wrote:The other thing you'll notice is that n=1-Tc/Th -- or that The maximum conversion efficiency is proportional to the difference in temperature between your hot and cold resovoirs.

Given that it's possible to use heat pumps to shift the heat back (and that the inefficiency of the heat pump just creates more heat that can be reclaimed), the efficiency of both the heat engine and the heat pump are irrelevant. For example, you could have 3 objects (CPU, heat store and cold store) where heat pumps are used to ensure that the temperatures of the CPU and cold store remain constant (by pumping excess heat into the heat store).

Mostly, there are only 2 ways to show that this setup isn't possible. Either you prove that conservation of energy is false (e.g. energy is destroyed), or you prove that it's impossible to prevent energy from escaping out of an isolated system.

The energy required to pump heat against a temperature gradient ΔT is greater than the energy that a carnot engine can recover from temperature gradient ΔT. In other words, your heat pump would consume all the energy from your carnot engine in order to not maintain the temperature gradient.

The energy required to pump heat against temperature... is stolen by invisible magic ninjas riding unicorns when you're not looking? You're attempting to prove the law of conservation of energy is false. That energy doesn't vanish, so where do you think it goes?

Also note that I strongly suspect you've screwed that up by confusing "is greater than" with "is not less than".


Cheers,

Brendan

Brendan wrote:Hi,

Owen wrote:

Brendan wrote:"The temperature of the cosmic microwave background radiation gives a practical lower limit to the energy consumed to perform computation of approximately 4kT per state change, where T is the temperature of the background (about 3 kelvins), and k is the Boltzmann constant. While a device could be cooled to operate below this temperature, the energy expended by the cooling would offset the benefit of the lower operating temperature."

I can't see what any of this has to do with what I wrote. What I wrote has nothing to do with temperatures at all. For a simple example, imagine a system of iron balls being pushed by electro-magnets made out of superconductors in a perfect vacuum (energy converted from electricity to momentum, and energy converted from momentum to electricity).

And if you do this experiment you fill find that, yes, there is no energy loss from the superconductors. However, you will also find that your magnets are heating up.

Owen wrote:(See Lloyd 1999)

This talks about speed of computation. It has no relevance.

See section Box: The role of thermodynamics in computation..

Brendan wrote:

Owen wrote:(Or: You can't break even except at absolute zero, and you can't ever reach absolute zero)

Also assumes temperature is involved in some way.

Of course it does. Temperature increases entropy. Entropy increases errors. You need to expend energy to minimize entropy in order to reject errors.

Brendan wrote:

Owen wrote:

Brendan wrote:You already stated that CPUs convert 100% of electrical energy into heat energy (I implicitly agree). Converting heat back into some other form of energy (e.g. electricity) is the only part where we disagree, which is what the Carnot engine does.

The Carnot engine converts a difference in temperatures to energy, not heat.

Same end result.

No it isn't, because in the process your heat sink is warming up. (The entropy of your heat sink is increasing. While energy is conserved, the entropy of a closed system can only ever increase

Brendan wrote:

Owen wrote:

Brendan wrote:Given that it's possible to use heat pumps to shift the heat back (and that the inefficiency of the heat pump just creates more heat that can be reclaimed), the efficiency of both the heat engine and the heat pump are irrelevant. For example, you could have 3 objects (CPU, heat store and cold store) where heat pumps are used to ensure that the temperatures of the CPU and cold store remain constant (by pumping excess heat into the heat store).

Mostly, there are only 2 ways to show that this setup isn't possible. Either you prove that conservation of energy is false (e.g. energy is destroyed), or you prove that it's impossible to prevent energy from escaping out of an isolated system.

The energy required to pump heat against a temperature gradient ΔT is greater than the energy that a carnot engine can recover from temperature gradient ΔT. In other words, your heat pump would consume all the energy from your carnot engine in order to not maintain the temperature gradient.

The energy required to pump heat against temperature... is stolen by invisible magic ninjas riding unicorns when you're not looking? You're attempting to prove the law of conservation of energy is false. That energy doesn't vanish, so where do you think it goes?

Into the hot reservoir.

Brendan wrote:Also note that I strongly suspect you've screwed that up by confusing "is greater than" with "is not less than".

Sorry, I will confess a mistake: The Carnot engine is a theoretical model which defines a maximally efficient reversible engine (In my defense, it's been a long time since I've had to deal with Carnot Engines). That is, yes, by injecting energy into a Carnot engine, you could indeed pump energy from cold to hot with the same efficiency as it would extract energy from the process. If you hooked up one of these to the other, you would produce a perpetual motion machine.

Of course, a Carnot engine is an idealized engine. You cannot actually build a reversible engine, because it is impossible for a real material to undergo an isentropic change of temperature. What this means, in other words, is that the entropy of the system must increase in the process.

All heat engines and pumps you can produce have η different from that of a Carnot engine. Actually, for an engine, η must be less than that of a Carnot engine; meanwhile, for a heat pump, η must be higher (Heat pumps normally use a figure called the Coefficient of Performance, which when operating against the thermal gradient is 1/η). If you want, go and do the calculations for what happens when this isn't true; what you will find is that you have just violated the 2nd law of thermodynamics (i.e. conservation of energy)

Anyway, you can go and do the calculations for this, and what you will find for ηengine < ηpump is that your hot reservoir is getting colder, and your cold reservoir is getting hotter...

Of course, eventually, Tc == Th will occur, and (1 - Tc/Th) will equal zero, and therefore even if you did have a perfect engine you would be unable to extract energy because you no longer have a temperature gradient to extract it from.

Which is good. We Physicists don't like having random perpetual motion machines randomly running around in perpetuity.

Hi,

Owen wrote:

Brendan wrote:

Owen wrote:"The temperature of the cosmic microwave background radiation gives a practical lower limit to the energy consumed to perform computation of approximately 4kT per state change, where T is the temperature of the background (about 3 kelvins), and k is the Boltzmann constant. While a device could be cooled to operate below this temperature, the energy expended by the cooling would offset the benefit of the lower operating temperature."

I can't see what any of this has to do with what I wrote. What I wrote has nothing to do with temperatures at all. For a simple example, imagine a system of iron balls being pushed by electro-magnets made out of superconductors in a perfect vacuum (energy converted from electricity to momentum, and energy converted from momentum to electricity).

And if you do this experiment you fill find that, yes, there is no energy loss from the superconductors. However, you will also find that your magnets are heating up.

Wrong. The only heat is from resistance (which is why there has to be superconductors with no resistance).

Owen wrote:

Brendan wrote:

Owen wrote:(See Lloyd 1999)

This talks about speed of computation. It has no relevance.

See section Box: The role of thermodynamics in computation..

Sorry - you're right. There was a little piece that is relevant. It's this part:

"In 1973, Bennett28−30 showed that all computations could be performed using reversible logical operations only. Consequently, by Landauer’s principle, computation does not require dissipation. (Earlier work by Lecerf27 had anticipated the possibility of reversible computation, but not its physical implications. Reversible computation was discovered independently by Fredkin and Toffoli31.) The energy used to perform a logical operation can be ‘borrowed’ from a store of free energy such as a battery, ‘invested’ in the logic gate that performs the operation, and returned to storage after the operation has been performed, with a net ‘profit’ in the form of processed information. Electronic circuits based on reversible logic have been built and exhibit considerable reductions in dissipation over conventional reversible circuits33−35 ."

Owen wrote:

Brendan wrote:

Owen wrote:(Or: You can't break even except at absolute zero, and you can't ever reach absolute zero)

Also assumes temperature is involved in some way.

Of course it does. Temperature increases entropy. Entropy increases errors. You need to expend energy to minimize entropy in order to reject errors.

Of course it does (but only if you're begging the question). Temperature increases entropy (but only thermodynamic entropy, which is only related to information entropy by fantasy). Entropy increases errors (for an unknown type of "errors" which are unlikely to matter). You need to expend energy to minimize entropy in order to reject errors (which is entirely false - to reject errors you want to increase redundancy and increase information entropy, but you also need to assume that errors are possible to begin with for no reason whatsoever).

Owen wrote:

Brendan wrote:

Owen wrote:The Carnot engine converts a difference in temperatures to energy, not heat.

Same end result.

No it isn't, because in the process your heat sink is warming up. (The entropy of your heat sink is increasing. While energy is conserved, the entropy of a closed system can only ever increase

You're assuming the heat sink is warming up here; and then apologising for assuming that the heat sink is warming up in your next paragraph...

Owen wrote:Sorry, I will confess a mistake: The Carnot engine is a theoretical model which defines a maximally efficient reversible engine (In my defense, it's been a long time since I've had to deal with Carnot Engines). That is, yes, by injecting energy into a Carnot engine, you could indeed pump energy from cold to hot with the same efficiency as it would extract energy from the process. If you hooked up one of these to the other, you would produce a perpetual motion machine.

Actually, the physicists have rigged the definitions of "perpetual motion machine" to ensure it's impossible. If you take a look you'll see that to qualify as a perpetual motion machine it has to be capable of doing "work", and that they've defined "work" as energy leaving the system. With these definitions, a perpetual motion machine is impossible (it defies the law of conservation of energy, as energy leaving the system has to come from somewhere). Our system doesn't have any energy leaving, therefore (using this definition of "work") it doesn't do any work, therefore it's also not a perpetual motion machine (it's just a machine that runs perpetually).


Cheers,

Brendan

Brendan wrote:Hi,

Owen wrote:

Brendan wrote:I can't see what any of this has to do with what I wrote. What I wrote has nothing to do with temperatures at all. For a simple example, imagine a system of iron balls being pushed by electro-magnets made out of superconductors in a perfect vacuum (energy converted from electricity to momentum, and energy converted from momentum to electricity).

And if you do this experiment you fill find that, yes, there is no energy loss from the superconductors. However, you will also find that your magnets are heating up.

Wrong. The only heat is from resistance (which is why there has to be superconductors with no resistance).

A metallic object being accelerated by a magnetic field is experiencing a change in the magnetic field, which will cause current to flow (by magnetic induction). Therefore, your iron balls will be heated.

(If your balls were themselves superconductors, they would reject the magnetic field until its' strength was sufficient for them to undergo phase transitions at which they would cease to be semiconductors)

Brendan wrote:

Owen wrote:

Brendan wrote:This talks about speed of computation. It has no relevance.

See section Box: The role of thermodynamics in computation..

Sorry - you're right. There was a little piece that is relevant. It's this part:

"In 1973, Bennett28−30 showed that all computations could be performed using reversible logical operations only. Consequently, by Landauer’s principle, computation does not require dissipation. (Earlier work by Lecerf27 had anticipated the possibility of reversible computation, but not its physical implications. Reversible computation was discovered independently by Fredkin and Toffoli31.) The energy used to perform a logical operation can be ‘borrowed’ from a store of free energy such as a battery, ‘invested’ in the logic gate that performs the operation, and returned to storage after the operation has been performed, with a net ‘profit’ in the form of processed information. Electronic circuits based on reversible logic have been built and exhibit considerable reductions in dissipation over conventional reversible circuits33−35 ."

Owen wrote:Of course it does. Temperature increases entropy. Entropy increases errors. You need to expend energy to minimize entropy in order to reject errors.

Of course it does (but only if you're begging the question). Temperature increases entropy (but only thermodynamic entropy, which is only related to information entropy by fantasy). Entropy increases errors (for an unknown type of "errors" which are unlikely to matter). You need to expend energy to minimize entropy in order to reject errors (which is entirely false - to reject errors you want to increase redundancy and increase information entropy, but you also need to assume that errors are possible to begin with for no reason whatsoever).

This entropy takes the form of spontaneous bit errors (e.g. the computation 1 AND 1 returning 0) due to classically forbidden quantum transitions (Modern processors already have to deal with this - by redundancy (i.e. using many electrons to represent a bit), because at modern process geometries electrons have an annoying habit of tunneling through the insulating gaps between conductors)

Brendan wrote:

Owen wrote:No it isn't, because in the process your heat sink is warming up. (The entropy of your heat sink is increasing. While energy is conserved, the entropy of a closed system can only ever increase

You're assuming the heat sink is warming up here; and then apologising for assuming that the heat sink is warming up in your next paragraph...

Of course the heat sink is warming up! Extracting energy from a thermal gradient by necessity involves moving energy along that thermal gradient!

The heat engine is warming up the cold heat sink, while the heat pump is attempting to move this heat back to the hot heat sink... But the amount of energy the heat engine is putting into the cold heat sink exceeds the amount that the heat pump is able to extract.

Brendan wrote:

Owen wrote:Sorry, I will confess a mistake: The Carnot engine is a theoretical model which defines a maximally efficient reversible engine (In my defense, it's been a long time since I've had to deal with Carnot Engines). That is, yes, by injecting energy into a Carnot engine, you could indeed pump energy from cold to hot with the same efficiency as it would extract energy from the process. If you hooked up one of these to the other, you would produce a perpetual motion machine.

Actually, the physicists have rigged the definitions of "perpetual motion machine" to ensure it's impossible. If you take a look you'll see that to qualify as a perpetual motion machine it has to be capable of doing "work", and that they've defined "work" as energy leaving the system. With these definitions, a perpetual motion machine is impossible (it defies the law of conservation of energy, as energy leaving the system has to come from somewhere). Our system doesn't have any energy leaving, therefore (using this definition of "work") it doesn't do any work, therefore it's also not a perpetual motion machine (it's just a machine that runs perpetually).

Where have you constructed this hypothetical machine? I see lots of heat flowing around, until entropy wins, both the hot and cold portions of the machine are at equal temperature, and all motion ceases.

P.S. the requirement to do work is required to disqualify, say, a slab of rock in a closed system from being a perpetual motion machine.

Hi,

Owen wrote:

Brendan wrote:

Owen wrote:And if you do this experiment you fill find that, yes, there is no energy loss from the superconductors. However, you will also find that your magnets are heating up.

Wrong. The only heat is from resistance (which is why there has to be superconductors with no resistance).

A metallic object being accelerated by a magnetic field is experiencing a change in the magnetic field, which will cause current to flow (by magnetic induction). Therefore, your iron balls will be heated.

Nope. The amount of induced voltage depends on the direction that the conductor is moving. If the conductor is moving across the magnetic field you get the maximum induced voltage (and highest eddy currents, and highest heat). In our case the conductor is moving away from the magnetic field (not across it), so you get the minimum induced voltage, which is zero, and therefore no eddy currents and no heat.

Owen wrote:

Brendan wrote:

Owen wrote:Of course it does. Temperature increases entropy. Entropy increases errors. You need to expend energy to minimize entropy in order to reject errors.

Of course it does (but only if you're begging the question). Temperature increases entropy (but only thermodynamic entropy, which is only related to information entropy by fantasy). Entropy increases errors (for an unknown type of "errors" which are unlikely to matter). You need to expend energy to minimize entropy in order to reject errors (which is entirely false - to reject errors you want to increase redundancy and increase information entropy, but you also need to assume that errors are possible to begin with for no reason whatsoever).

This entropy takes the form of spontaneous bit errors (e.g. the computation 1 AND 1 returning 0) due to classically forbidden quantum transitions (Modern processors already have to deal with this - by redundancy (i.e. using many electrons to represent a bit), because at modern process geometries electrons have an annoying habit of tunneling through the insulating gaps between conductors)

For the "iron balls" example, no amount of heat is going to make my iron balls gain momentum. For the "normal CPU with heat recyclers" example, the CPUs are no different to the CPUs we're using now (we know they work properly most of the time).

Owen wrote:

Brendan wrote:

Owen wrote:No it isn't, because in the process your heat sink is warming up. (The entropy of your heat sink is increasing. While energy is conserved, the entropy of a closed system can only ever increase

You're assuming the heat sink is warming up here; and then apologising for assuming that the heat sink is warming up in your next paragraph...

Of course the heat sink is warming up! Extracting energy from a thermal gradient by necessity involves moving energy along that thermal gradient!

So? Move energy along that thermal gradient, then pump it back!

Owen wrote:The heat engine is warming up the cold heat sink, while the heat pump is attempting to move this heat back to the hot heat sink... But the amount of energy the heat engine is putting into the cold heat sink exceeds the amount that the heat pump is able to extract.

Wrong.

Think of it like this. Each second:

• the heat engine converts 4 units of heat from the CPU into 3 units of electricity and 1 unit of heat at the heatsink (note: 4 units in, 3+1 units out)
• the heat pump converts 2 units of electricity and 1 unit of heat from the heatsink into 3 units of heat at the CPU (note: 2+1 units in, 3 units out)
• the CPU converts 1 unit of electricity into 1 unit of heat (note: 1 unit in, 1 unit out)

In total, every second:

• the CPU and heat pump consume 2+1 units of electricity, and the heat engine generates 3 units of electricity (the total amount of electrical energy remains constant)
• the heat engine takes 4 units of heat from the CPU and the CPU and the heat pump put 1+3 units of heat back in (the CPU's temperature remains constant)
• the heat engine adds 1 unit of heat to the heatsink, and the heat pump removes 1 unit of heat from the heatsink (the heatsink's temperature remains constant)

Also note that the heat engine is only 75% efficient, and the heat pump is also only 75% efficient. If you assume the CPU is running at 27 degrees Celsius (300 degrees Kelvin) and the heatsink is at 3 Kelvin (your "background temperature"), neither heat engine nor heat pump are near their theoretical maximum efficiency.


Cheers,

Brendan

Brendan wrote:Hi,

Owen wrote:

Brendan wrote:Wrong. The only heat is from resistance (which is why there has to be superconductors with no resistance).

A metallic object being accelerated by a magnetic field is experiencing a change in the magnetic field, which will cause current to flow (by magnetic induction). Therefore, your iron balls will be heated.

Nope. The amount of induced voltage depends on the direction that the conductor is moving. If the conductor is moving across the magnetic field you get the maximum induced voltage (and highest eddy currents, and highest heat). In our case the conductor is moving away from the magnetic field (not across it), so you get the minimum induced voltage, which is zero, and therefore no eddy currents and no heat.

In that case, as you should know from Newton's Second Law, equal and opposite momentum will be imparted upon the superconductors.

If they are separated in space, they will accelerate away from each other with each iteration (until the iron ball stops passing between them). The potential energy of the system is reduced with each iteration.

If they are anchored firmly to something (Say, the Earth), it will absorb the force and, by friction, heat up.

Brendan wrote:

Owen wrote:

Brendan wrote:Of course it does (but only if you're begging the question). Temperature increases entropy (but only thermodynamic entropy, which is only related to information entropy by fantasy). Entropy increases errors (for an unknown type of "errors" which are unlikely to matter). You need to expend energy to minimize entropy in order to reject errors (which is entirely false - to reject errors you want to increase redundancy and increase information entropy, but you also need to assume that errors are possible to begin with for no reason whatsoever).

This entropy takes the form of spontaneous bit errors (e.g. the computation 1 AND 1 returning 0) due to classically forbidden quantum transitions (Modern processors already have to deal with this - by redundancy (i.e. using many electrons to represent a bit), because at modern process geometries electrons have an annoying habit of tunneling through the insulating gaps between conductors)

For the "iron balls" example, no amount of heat is going to make my iron balls gain momentum. For the "normal CPU with heat recyclers" example, the CPUs are no different to the CPUs we're using now (we know they work properly most of the time).

Gotcha. For your nonphysically valid example, we are using traditional CPUs (whereby the random bit error rate is negligible because they have low quantum efficiencies). Somehow we got sidetracked by perpetual motion machines. Hopefully this sojourn can soon conclude:

Brendan wrote:

Owen wrote:

Brendan wrote:You're assuming the heat sink is warming up here; and then apologising for assuming that the heat sink is warming up in your next paragraph...

Of course the heat sink is warming up! Extracting energy from a thermal gradient by necessity involves moving energy along that thermal gradient!

So? Move energy along that thermal gradient, then pump it back!

It doesn't work like that!

Brendan wrote:

Owen wrote:The heat engine is warming up the cold heat sink, while the heat pump is attempting to move this heat back to the hot heat sink... But the amount of energy the heat engine is putting into the cold heat sink exceeds the amount that the heat pump is able to extract.

Wrong.

Think of it like this. Each second:

• the heat engine converts 4 units of heat from the CPU into 3 units of electricity and 1 unit of heat at the heatsink (note: 4 units in, 3+1 units out)
• the heat pump converts 2 units of electricity and 1 unit of heat from the heatsink into 3 units of heat at the CPU (note: 2+1 units in, 3 units out)
• the CPU converts 1 unit of electricity into 1 unit of heat (note: 1 unit in, 1 unit out)

In total, every second:

• the CPU and heat pump consume 2+1 units of electricity, and the heat engine generates 3 units of electricity (the total amount of electrical energy remains constant)
• the heat engine takes 4 units of heat from the CPU and the CPU and the heat pump put 1+3 units of heat back in (the CPU's temperature remains constant)
• the heat engine adds 1 unit of heat to the heatsink, and the heat pump removes 1 unit of heat from the heatsink (the heatsink's temperature remains constant)

Also note that the heat engine is only 75% efficient, and the heat pump is also only 75% efficient. If you assume the CPU is running at 27 degrees Celsius (300 degrees Kelvin) and the heatsink is at 3 Kelvin (your "background temperature"), neither heat engine nor heat pump are near their theoretical maximum efficiency.

The maximum theoretical thermodynamic efficiency of the heat thermal engine is η = 1 - Tc/Th, in this case 0.99. So far so good!

The maximum theoretical efficiency of the heat pump is given by CP= 1/η, so between these reservoirs is 1.010101

Unfortunately, you have calculated the efficiency of your heat pump wrong, because the efficiency of a heat pump is defined as Q/W, where Q is the energy moved to the hot reservoir. You're imparting 3 units of heat into the hot reservoir for every 1 unit of work, giving an efficiency of your heat pump of CP=1.5.

(We use CP rather than η for heat pumps because it makes sense to talk about "Energy imparted on the heat source" rather than "Work per unit of heat imparted into the hotter sump". You can do the maths the other way around - just η is the minimum value for a heat pump, as opposed to the maximum value for a heat engine. η for your heat pump is 2/3, less than 0.99.)

Quite clearly, 1.5 > 1.010101. I rest assured that I can sleep soundly tonight, knowing that perpetual computational devices will not brute force my 2048-bit RSA keys.