Van Winter Memorial Lecture in Mathematical Physics
Professor Elliot Lieb of Princeton University will give a special
combined Mathematics/Theoretical Physics seminar on Monday, September 10, 2001
and deliver the inaugural Van Winter Memorial Lecture in Mathematical Physics
on Tuesday, September 11, 2001.
Van Winter Memorial Lecture in Mathematical Physics
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Professor Elliot Lieb, Princeton University
"The Quantum-Mechanical World View:
A Remarkably Successful but Still
Incomplete Theory"
Tuesday, September 11, 2001
Chemistry-Physics Building, Room 153, 5:00 PM
Abstract:
This talk will be about some important, unsolved problems of a mathematical
nature connected with the quantum mechanical many-body theory. It will
center on the stability of matter problem and how this is connected to
the largely unsolved problem of quantum electrodynamics. The historical
background and the present status of the subject will be reviewed.
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Special Combined Mathematics/Theoretical Physics Seminar
Professor Elliot Lieb, Princeton University
"The Mathematics of the Second Law of Thermodynamics"
Monday, September 10, 2001
Chemistry-Physics Building, Room CP 155, 4:00 PM
Abstract
The essence of the second law is the `entropy principle' which
states that all processes can be quantified by an entropy function on the space
of all equilibrium states, whose increase is a necessary and sufficient condition
for a process to occur. It is one of the few really fundamental physical laws
(in the sense that no deviation, however tiny, is permitted) and its consequences
are far reaching. Since the entropy principle is independent of any statistical
mechanical model, it ought to be derivable from a few logical principles without
recourse to Carnot cycles, ideal gases and other assumptions about such things
as `heat', `hot' and `cold', `temperature', `reversible processes', etc., as
is usually done. Also, the well-known Boltzmann/Shannon formula for entropy,
is irrelevant since statistical mechanical modeling is irrelevant.
In this lecture the foundations of the subject and the construction of entropy
from a few simple axioms will be presented. The axioms basically are those of
a preorder, except for one additional axiom called `the comparison hypothesis'.
It can be said that this theory solves the question: `When is a preorder on
a set equivalent to a monotone function on the set ?' As such, it could conceivably
be useful in other areas of mathematics. No prior knowledge of thermodynamics
or physics is needed for this lecture. (reference: AMS Notices, 45,
571-581 (1998) and Physics Today, 53, 32-37 (2000)).
The Van Winter Lectures in Mathematical Physics
This lecture series honors the memory of Clasine Van Winter, who held a professorship
in the Department of Mathematics and the Department of Physics and Astronomy
from 1968 to her retirement in 1999. Professor Van Winter specialized in the
study of multiparticle quantum systems; her contributions include the Weinberg-Van
Winter equations for a multiparticle quantum system, derived independently by
Professor Van Winter and Professor Steven Weinberg, and the so-called HVZ Theorem
which characterizes the essential spectrum of multiparticle quantum systems.
She died in October of 2000.
The Van Winter endowment sponsors an annual lecture by a distinguished mathematical
physicist chosen by the chairs of the Department of Mathematics and the Department
of Physics and Astronomy in consultation with their respective faculties. The
endowment is jointly held by the Department of Mathematics and the Department
of Physics and Astronomy.
Professor Elliott Lieb
Elliott Lieb received his Ph. D. in Mathematical Physics from the University
of Birmingham in 1956. He is Professor of Mathematics and Physics at Princeton
University. He is a member of the National Academy of Sciences and a Fellow
of the American Physical Society, and a past president of the International
Association for Mathematical Physics. He held Guggenheim Fellowships in 1972
and 1978 and has received honorary doctorates from the University of Copenhagen
and the Ecole Polytechnique Fédérale-Lausanne. Other honors include
the Heineman Prize in Mathematical Physics, the Birkhoff Prize in Applied Mathematics,
the Max Planck Medal of the German Physical Society, and the Schock Prize in
Mathematics from the Swedish Academy of Sciences. He has authored over 250 articles
and books.
