UNIST Professors Kim Chae-woon, Kim Jae-up, and Kim Cheol-min Develop New Process Allocation Principle Applying Boltzmann Distribution
Joint Research with Ulsan University Economics PhD Park Ji-won, Published in Scientific Reports
What is fair distribution? A physicist, an economist, and a child dividing a cake. The research team introduced this as an illustration related to a study that signifies applying principles of physics to distribution problems.
[Asia Economy Yeongnam Reporting Headquarters Reporter Kim Yong-woo] An intriguing study has emerged that approaches the issue of ‘fair distribution,’ traditionally considered a social and economic problem, from the perspective of energy in physics.
The researchers solved the problem of fair distribution by finding distribution principles through physics.
“We focused on achieving fair distribution through the ‘natural allocation’ of resources rather than the participants’ subjective ‘satisfaction.’ This is a completely new distribution principle applying the ‘Boltzmann distribution,’ which physical systems in equilibrium naturally follow with the highest probability.”
Ulsan National Institute of Science and Technology (UNIST) announced on the 10th that a team consisting of Professors Kim Chae-woon, Kim Jae-up, and Kim Cheol-min from the Department of Physics and Dr. Park Ji-won from the Department of Economics at the University of Ulsan jointly developed a ‘fair distribution principle inspired by physics.’
Since it is based on the Boltzmann distribution from statistical physics, they named it ‘The Boltzmann Fair Division.’
Professor Kim Chae-woon, who participated in the study, explained, “It is practically impossible to satisfy all stakeholders placed in different situations when distributing limited resources. If we base the principle on participants’ subjective ‘satisfaction,’ it is difficult to derive a rational ‘principle of distribution.’ However, if we change the perspective and consider the ‘natural distribution of resources’ as the standard of fairness, the story changes,” explaining the background of applying physics to the economic concept of distribution.
The Boltzmann distribution represents the natural energy state distribution with the highest probability for atoms or molecules belonging to a physical system in thermal equilibrium.
The velocity distribution of air molecules in a room set at a constant temperature is also based on the Boltzmann distribution. Introducing the concept of ‘natural distribution’ implied by the Boltzmann distribution into economics can serve as the foundation for a fair distribution principle.
To this end, the research team substituted the physical concepts used in the Boltzmann distribution?‘particles,’ ‘energy states,’ and ‘energy values’?with economic concepts that should be considered in fair distribution.
Particles were replaced with ‘limited resources,’ energy states with ‘participants,’ and energy values with ‘participants’ contribution to resource production.’
By applying it this way, limited resources are designed to be distributed most naturally and fairly according to participants’ contributions.
Dr. Park Ji-won explained, “The Boltzmann Fair Division, which allocates resources reflecting realistic factors such as participants’ contributions and preferences, determines the degree of distribution spread by a constant (β value) that embodies the concept of ‘social temperature.’”
He also explained, “This constant value can be optimized by combining it with the utilitarian philosophy of ‘the greatest happiness for the greatest number.’”
Professor Kim Chae-woon said, “If the value of the ‘social temperature’ embedded in the Boltzmann Fair Division is high, a warm community forms where resources are broadly distributed to participants; conversely, if it is low, a harsh and cold society emerges where a few participants monopolize resources.”
Professor Kim added, “It could serve as a benchmark when establishing policies for our society to move toward a warmer community.”
The Boltzmann Fair Division devised in this study was generalized to be applicable to various and complex problems requiring the distribution of limited resources to many participants in different situations.
Attention is focused on whether this research can be utilized in reality to alleviate the phenomenon of wealth polarization or solve various problems requiring international cooperation.
This research was conducted with support from the Samsung Future Technology Development Foundation, and the results were published in ‘Scientific Reports.’
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