News Article
Entropy, Fluctuations And Nanotech
A warning to over-optimistic nanotechnologists comes from the world of basic
research where Australian scientists have produced measurable violations of
the
On the basis of the Second Law, one is not surprised when one's coffee/tea
goes cold. In other words, the temperatures of hot things put in a cold
enivronment lose heat and cold things put in a hot environment gain heat.
These facts give an "arrow" to time. Looked at with the clock running
backwards one could just sit a cold cup of coffee on the table and it would
heat up! (One would then take it to the milk carton, which would then suck
the milk out of the cup . . .)
However, the basic laws of physics don't seem to have the same time
directionality. All the interactions we know of for certain except the "Weak
Force" (i.e. Gravity, Strong Force, Electromagnetism) are completely time
reversible. Even, the Weak interaction satisfies a modified time
reversibility where all particles are converted into anti-particles and the
whole is reflected in a mirror (called TCP or PCT invariance). What gives?
The laws of thermodynamics - and the Second Law, in particular - are the
result of empirical observations on large systems made up of huge numbers of
parts. For example, 12g of carbon contains 6E23 (Avogadro's number, six with
23 zeros) atoms. The theories of "Statistical Mechanics" use this hugeness
to explain thermodynamics.
So why does a hot cup of coffee get cold? The energy in the cup can be
spread through the coffee atoms in a large number of ways that look the same
to us macroscopic beings. The system's components jiggle around and go
through a large number of these ways over time.
But the system doesn't just exchange energy with itself. Energy is absorbed
from and emitted into the environment. Energy is conserved (First Law). If
the environment is colder than the coffee, emission will predominate over
absorbtion. If the two processes are equal on average the two systems will
be in "equillibrium" - their temperatures are the same. Some even describe
this as being the "Zeroth Law".
Whether emission predominates over absorbtion is generally determined by
what is more probable. A system in a less probable state will likely move to
a more probable state. This is how a hot coffee is thought to go cold. It
shares its excess of energy with the colder environment. In Statistical
Mechanics the probability of states can be related to the "entropy". More
probable states have higher entropy.
However, for small systems it is possible for the total entropy to decrease
for short periods of time. These events are called "fluctuations".
How does this relate to nanotechnology. The PRL paper starts: "Inventors and
engineers endeavour to scale-down machines and engines to nanometre sizes
for a wide range of technological purposes. However there is a fundamental
limitation to miniaturisation as small engines are not simple rescaled
versions of their larger counterparts. If the work performed during the duty
cycle of any machine is comparable to thermal energy per degree of freedom,
then one can expect that the machine will operate in 'reverse' over small
timescales. That is, heat energy from the surroundings will be converted
into useful work allowing the engine to run backwards. For larger engines,
we would describe this as a violation of the Second Law of Thermodynamics,
as entropy is consumed rather than generated."
So it is not just the small size, but faster operation (short timescales)
that can create unusual effects. "The Fluctuation Theorem points out that as
these thermodynamic engines are made smaller and as the time of operation is
made shorter, these engines are not simple scaled-down versions of their
larger counterparts. As they become smaller, the probability that they will
run thermodynamically in reverse inescapably becomes greater. Consequently,
these results imply that the Fluctuation Theorem has important ramifications
for nanotechnology and indeed for how life itself functions."
The Australian scientists studied how colloidal particles (latex) in water
behaved over short timescales in an optical trap that was translated
relative to the water. Entropy consuming trajectories were found for
micron-sized particles over times of the order of seconds.
goes cold. In other words, the temperatures of hot things put in a cold
enivronment lose heat and cold things put in a hot environment gain heat.
These facts give an "arrow" to time. Looked at with the clock running
backwards one could just sit a cold cup of coffee on the table and it would
heat up! (One would then take it to the milk carton, which would then suck
the milk out of the cup . . .)
However, the basic laws of physics don't seem to have the same time
directionality. All the interactions we know of for certain except the "Weak
Force" (i.e. Gravity, Strong Force, Electromagnetism) are completely time
reversible. Even, the Weak interaction satisfies a modified time
reversibility where all particles are converted into anti-particles and the
whole is reflected in a mirror (called TCP or PCT invariance). What gives?
The laws of thermodynamics - and the Second Law, in particular - are the
result of empirical observations on large systems made up of huge numbers of
parts. For example, 12g of carbon contains 6E23 (Avogadro's number, six with
23 zeros) atoms. The theories of "Statistical Mechanics" use this hugeness
to explain thermodynamics.
So why does a hot cup of coffee get cold? The energy in the cup can be
spread through the coffee atoms in a large number of ways that look the same
to us macroscopic beings. The system's components jiggle around and go
through a large number of these ways over time.
But the system doesn't just exchange energy with itself. Energy is absorbed
from and emitted into the environment. Energy is conserved (First Law). If
the environment is colder than the coffee, emission will predominate over
absorbtion. If the two processes are equal on average the two systems will
be in "equillibrium" - their temperatures are the same. Some even describe
this as being the "Zeroth Law".
Whether emission predominates over absorbtion is generally determined by
what is more probable. A system in a less probable state will likely move to
a more probable state. This is how a hot coffee is thought to go cold. It
shares its excess of energy with the colder environment. In Statistical
Mechanics the probability of states can be related to the "entropy". More
probable states have higher entropy.
However, for small systems it is possible for the total entropy to decrease
for short periods of time. These events are called "fluctuations".
How does this relate to nanotechnology. The PRL paper starts: "Inventors and
engineers endeavour to scale-down machines and engines to nanometre sizes
for a wide range of technological purposes. However there is a fundamental
limitation to miniaturisation as small engines are not simple rescaled
versions of their larger counterparts. If the work performed during the duty
cycle of any machine is comparable to thermal energy per degree of freedom,
then one can expect that the machine will operate in 'reverse' over small
timescales. That is, heat energy from the surroundings will be converted
into useful work allowing the engine to run backwards. For larger engines,
we would describe this as a violation of the Second Law of Thermodynamics,
as entropy is consumed rather than generated."
So it is not just the small size, but faster operation (short timescales)
that can create unusual effects. "The Fluctuation Theorem points out that as
these thermodynamic engines are made smaller and as the time of operation is
made shorter, these engines are not simple scaled-down versions of their
larger counterparts. As they become smaller, the probability that they will
run thermodynamically in reverse inescapably becomes greater. Consequently,
these results imply that the Fluctuation Theorem has important ramifications
for nanotechnology and indeed for how life itself functions."
The Australian scientists studied how colloidal particles (latex) in water
behaved over short timescales in an optical trap that was translated
relative to the water. Entropy consuming trajectories were found for
micron-sized particles over times of the order of seconds.