Seth LloydPaul Penfield, Jr.Massachusetts Institute of Technology
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The Second Law of Thermodynamics is one of science's priceless intellectual
achievements!
It is grounded in, and informs, fundamental issues:
. . . time reversibility, the nature of measurement, . . .
It is universal.
There is a non-conserved, monotonically increasing, quantity.
But as normally presented, entropy is difficult.
It is usually considered part of thermodynamics.
EE and CS students are not motivated to study it.
The Second Law, as usually stated, is only approximate.
We will cover information, of which entropy is part.
This matches today's student backgrounds and interests.
This leads to universal and exact form of the Second Law.
It serves the information age.
It gives students a useful model to help interpret the world.
It is found in different forms.
Kinetic
Potential
Electric
Magnetic
Chemical
. . .
It is conserved.
This property is so important that when a leak is found, we
invent a new form just to preserve it.
. . . heat, mass . . .
Energy can be moved in space and time.
You can design energy converters.
It has a quantitative theory.
The basic unit is the bit.
Arrays of bits can represent complex objects.
It is found in different forms.
Information we have
Information we don't have
Information we have is inherently subjective.
Information we don't have is also inherently subjective.
However, sometimes total information is not subjective.
Information is not conserved.
We lose track of things.
Noise is the enemy.
Information can be moved in space and time.
You can design information converters.
Entropy is information we don't have.
Entropy is therefore subjective.
Traditionally, entropy is a property of physical systems.
Avogadro's number = 6 x 10^23
With that many atoms there is lots of information you don't have.
So entropy is not very subjective (knowledge is only a few bits).
But things are changing.
Today we can manipulate bits with only a few atoms.
Semiconductor devices are pushing the quantum limits.
Note: Entropy is not the monotonic quantity in the Second Law of Thermodynamics.
Information is.
Entropy is only the information we don't have.
You can design information converters.
. . . quantum computers, Maxwell's Demon, measurements,
even steam engines . . .
Useful for
. . . Computing, Communications, Physical Systems . . .
Key notion is partitioning the universe.
Space
Observer / observed
Visibility filter
Known / unknown
Abstraction level
Type
. . . electrical, kinetic, chemical . . .
Difficult issues need to be addressed.
Information may be correlated across the partition.
Things may be irreversible.
Analogy to Energy
We believe so!
There is no need for calculus.
Of course only limited depth is possible at the freshman level.
We will rely on student background and interest in information.
Today all students are computer literate.
This is, after all, the information age.
Information is now one of engineering's foundational sciences:
. . . Physics, Chemistry, Biology, Information . . .
Mathematics is also needed, to provide notation, concepts, and tools for many fields.
Topics
The digital abstraction and the bit
Representation of objects by fixed-length codes
. . . ASCII, genetic code . . .
Applications to computing
. . . Compression, LZ, GIF (reversible), JPEG (irreversible) . . .
Probability and variable-length codes
Maximum entropy technique for calculating probabilities
. . . Morse code, Huffman codes . . .
Applications to communications
Noise and irreversibility
Shannon theorems
Applications to physical systems
Boltzmann probability distribution
Second Law of Thermodynamics
Timetable
Informal seminar, Fall 1998
Serious course development, Fall 1999
Pilot offering, Spring 2000
Note writing, serious revisions, Fall 2000
First normal offering, Spring 2001
Dramatis Personae
Seth Lloyd, Department of Mechanical Engineering, MIT
His research interests include quantum computing.
He currently offers a similar senior-level course.
Paul Penfield, Jr., Department of Electrical Engineering and Computer Science, MIT
He has a background in thermodynamics, noise, & computing.
No longer Department Head, he can do fun stuff now.
Venue
First, MIT
Next, other engineering schools
If successful, general universities
Where does it fit at MIT?
Half-course slot is available in spring of freshman year.
The course cannot be required.
It will compete with other offerings.
It cannot be a prerequisite for anything else.
But it will be consistent with approaches taken in later courses.
They will have a new model with which to interpret the world.
A quantity that is monotonic (as opposed to constant)
They will see information everywhere they look.
Who needs it? Just about everybody!
Some engineers will use the concepts routinely.
Chemical engineers, specialists in communications or information processing
Others will use the concepts mainly for motivation.
Some science majors will need it.
Liberal arts majors need the broadening exposure.
This may be an excellent way to satisfy a science requirement.
Information may become the most important science in this information age.