"One of the most pressing economic and corporate governance issues of the day is how to determine fair pay packages for CEOs," said Venkat Venkatasubramanian, a professor of chemical engineering. "The proposed theory allows us to compute what the fair pay is for a CEO, including bonuses and stock options, under ideal conditions."

The ratio of CEO pay to the lowest employee salary has gone up from about 40-to-1 in the 1970s to as high as 344-to-1 in recent years in the United States. However, the ratio has remained around 20-to-1 in Europe and 11-to-1 in Japan, according to available data, he said.

Using the new analysis method, Venkatasubramanian estimated that the 2008 salaries of the top 35 CEOs in the United States were about 129 times their ideal fair salaries. CEOs in the Standard & Poor's 500 averaged about 50 times their fair pay, raising questions about the efficiency of the free market to properly determine fair CEO pay, he said.

"You might ask why a chemical engineer is concerned with economics and CEO salaries," Venkatasubramanian said. "Well, it turns out that the same concepts and mathematics used to solve problems in statistical thermodynamics and information theory also can be applied to economic issues, such as the determination of fair CEO salaries."

A key idea in his theory is the economic interpretation of the concept of entropy.
"There have been many attempts to find a suitable interpretation of entropy for economic systems without much success," Venkatasubramanian said. "Just as entropy is a measure of disorder in thermodynamics and uncertainty in information theory, what would entropy mean in economics?"

Venkatasubramanian identified entropy as a measure of "fairness" in economic systems, revealing a connection between statistical thermodynamics, information theory and economics.

"As we all know, fairness is a fundamental economic principle that lies at the foundation of the free and efficient market system," he said. "It is so vital to the proper functioning of the markets that we have regulations and watchdog agencies that break up and punish unfair practices such as monopolies, collusion and insider trading. Thus, it is eminently reasonable, indeed reassuring, to find that maximizing fairness, or maximizing entropy, is the condition for achieving economic equilibrium."

Using the new theory, the ideal pay distribution is determined to be "lognormal," a particular way of characterizing data patterns in probability and statistics.