WASHINGTON — Leo P. Kadanoff, one of the leading theoretical physicists of his era, whose work on phase transitions — the sudden shifts between different states of the same substance — exerted vast influence throughout science, died Oct. 26 in Chicago. He was 78.

His death from respiratory failure was announced by the University of Chicago, where he was a professor from 1978 until his retirement in 2003 and a former director of its Materials Research Center.

Phase transitions, such as those between steam and water and between water and ice, in which a single substance takes many forms, have intrigued scientists for centuries. Some have been well explained, but creating detailed explanations for some of the more complex transitions continued to challenge physicists until the last half of the 20th century.


Throughout the world of modern physics, Dr. Kadanoff was lauded as one of the foremost in delineating how even the most subtle and complex phase transitions occur. He was also credited with showing how the large-scale changes that are easily observable stem from microscopic changes beyond the reach of the senses.

The work he did showed great generality. He inspired progress throughout physics by demonstrating not just the solution to one problem or another but also by showing new approaches useful in attacking many problems.

In addition, Dr. Kadanoff focused his attention on behavior at the ''critical point,'' at which two phases of the same substance may coexist in precarious balance.

Only a few scientists have been credited with comparably significant work, and Dr. Kadanoff earned many of his profession's highest honors.

One was the 1999 National Medal of Science, which he received from President Clinton. The citation accompanying the medal recognized Dr. Kadanoff for discoveries with ''important applications in engineering, urban planning, computer science, hydrodynamics, biology, applied mathematics, and geophysics.''


He held the Isaac Newton medal, bestowed in London by the Institute of Physics and named for the man often called history's greatest scientist.

Associated with Dr. Kadanoff's name were techniques listed as scaling, universality, and renormalization. Scaling is to a considerable degree a matter of demonstrating similarities in the behavior of matter across the spectrum of scales, from the microscopic to the visible world.

Universality refers to the discovery of overarching similarities in the paths taken by different substances en route to phase change and their critical points. Renormalization entails creating a practical way of dealing mathematically with systems in which important values trend toward infinity.

Dr. Kadanoff was also credited with helping discover the algebraic terms needed to describe the complex processes he was studying. One term required raising a variable to the power ''y.'' The second term entailed raising the same variable to the power ''z.''

It was a great advance, but the values of the exponents remained unknown. Dr. Kadanoff recalled how matters stood by the mid-1960s: ''If we could but find y and z.''

Building on Dr. Kadanoff's work, physicist Kenneth G. Wilson solved the problem in 1971, putting forward what became known as the theory of the renormalization group. The work was rewarded by the 1982 Nobel Prize.

Dr. Kadanoff did not claim to be instantly overjoyed by Wilson's achievement. In fact, he acknowledged years later that he had initially been ''disappointed and angry.''

How, he recalled himself wondering, ''could someone else finish up the description of my beautiful world?''


But he said he came around eventually, happy that Wilson had put the finishing touches on ''an edifice of transcendent beauty and importance.''

In the years after his groundbreaking work on transitions, Dr. Kadanoff worked in a variety of fields that were often characterized by complex behaviors arising from simple starting points and interactions. These included chaos theory and the study of fractals.

In addition, he offered his views on matters in which science and the public sphere intersect. That meant commenting on such matters as the value of computers in urban planning as well as on intelligent design, a concept in which complexity is employed as an argument against evolution.

A New York City native, Leo Philip Kadanoff received bachelor's, master's, and doctoral degrees from Harvard University.

He later served on the faculties of the University of Illinois and Brown University.

His first marriage, to Diane Gordon, ended in divorce. Dr. Kadanoff leaves his wife, Ruth Ditzian-Kadanoff; three daughters; a stepdaughter; and four grandchildren.

When Dr. Kadanoff was asked whether in a second life he would become a physicist again, his answer was strongly in the affirmative. He said the field used his skill at mathematics, made contact with his environment, and made him feel ''that I understand how the world works.''