University of Arizona Research Illuminates How the Second Law Emerges in Quantum Systems
A recent publication in the journal Entropy highlights new theoretical insights into one of physics’ most fundamental principles, the Second Law of Thermodynamics, by examining how it emerges from the laws of quantum mechanics. The study, “Emergence of the 2nd Law in an Exactly Solvable Model of a Quantum Wire,” was authored by University of Arizona physicist Charles A. Stafford and his former doctoral student, Marco Antonio Jimenez‑Valencia.
Marco received his PhD in Physics from the University of Arizona in 2025, defending his dissertation in July. He is currently collaborating with scientists at the University of Sonora, continuing research that builds on his doctoral work. The study represents a key milestone in his early research career and reflects his contributions to foundational questions in quantum thermodynamics.
Making Sense of Energy, Entropy, and Measurement
The research addresses a long‑standing question in physics: how does the familiar macroscopic behavior described by the Second Law of Thermodynamics arise from an exact microscopic description governed by quantum mechanics? While the Second Law is readily demonstrated using statistical arguments, verifying it at the quantum level becomes significantly more difficult as systems are described with increasing precision.
As the authors describe:
“As remarked by Boltzmann, the Second Law of Thermodynamics is notable for the fact that it is readily proved using elementary statistical arguments, but becomes harder and harder to verify the more precise the microscopic description of a system. In this article, a new quantum formula for the flow of entropy is used to analyze how the 2nd Law of Thermodynamics emerges from a sequence of thermoelectric measurements in an exactly solvable model of a quantum wire under electric bias. In our exact microscopic description of the quantum dynamics, the conversion of electrical power into heat (and entropy) does not happen automatically. Instead, we show that this conversion process is complete only when a very large number of continuous thermoelectric measurements are performed on the wire, wherein the information obtained is not stored but is rejected as entropy into the wire.”
The figure accompanying the article depicts a quantum wire with a voltage applied between the source (S) and drain (D) electrodes, continuously monitored by a sequence of thermoelectric probes. The total entropy production approaches that predicted by the 2nd Law of Thermodynamics as the number of measurements increases.
Rather than assuming entropy production from the outset, the researchers demonstrate how it develops dynamically through measurement and information loss.
About the Stafford Research Group
Charles A. Stafford is a Professor of Physics at the University of Arizona, where he leads the Stafford research group. The group studies the dynamics and thermodynamics of driven and open quantum systems, bridging condensed matter physics, nanoscale transport, and quantum information science. Past and current research topics include quantum transport in mesoscopic systems, the stability of metal nanowires, quantum thermoelectricity, quantum thermometry, and condensed‑matter analogues of black hole physics.
More recently, the group’s work has focused on quantum thermodynamics, including nonlocal effects in quantum work and the flow of entropy in driven quantum systems. Stafford’s research has resulted in a substantial body of highly cited publications and multiple U.S. patents for quantum and nanoscale devices. Stafford is also widely recognized for strong mentorship of undergraduate and graduate students, earning both international research honors and university‑level teaching awards.
Broader Impact
By providing an exact, solvable quantum model for entropy production and Joule heating, this work deepens our understanding of how classical thermodynamic laws emerge from quantum mechanics. These insights are increasingly relevant as researchers develop nanoscale and quantum technologies where energy dissipation, measurement, and information flow cannot be taken for granted.
The full publication is available at:
https://doi.org/10.3390/e28030316