🔬 mesoscale physics

Ohm's law for information revealed by a skyrmion Maxwell's demon

This paper experimentally validates an Ohm's law for information by demonstrating that an information current driven by a skyrmion-based Maxwell's demon is proportional to information affinity, while also revealing necessary modifications to both Ohm's and Kirchhoff's laws to account for carrier interactions and current scattering in real information circuits.

Original authors: Soma Miki, Yoshishige Suzuki, Ryo Ishikawa, Yuki Hibino, Shunya Morishita, Hiroto Imanishi, Keigo Adachi, Yoichi Shiota, Takayuki Nozaki, Minori Goto, Hikaru Nomura, Shigemi Mizukami, Eiiti Tamura

Published 2026-09-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Soma Miki, Yoshishige Suzuki, Ryo Ishikawa, Yuki Hibino, Shunya Morishita, Hiroto Imanishi, Keigo Adachi, Yoichi Shiota, Takayuki Nozaki, Minori Goto, Hikaru Nomura, Shigemi Mizukami, Eiiti Tamura

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the age of artificial intelligence, the most pressing challenge for computing is not just making machines faster, but making them more efficient. Every calculation generates heat, and as devices shrink, this energy cost becomes a bottleneck. To solve this, scientists are looking to a branch of physics called information thermodynamics. This field explores the deep connection between information and energy, treating information not as an abstract concept, but as a physical quantity that can be moved and transformed, much like electricity or water. A central idea in this field is the "Maxwell's demon," a thought experiment from the 19th century where a tiny, intelligent being sorts particles to create order without expending energy, seemingly breaking the laws of physics. Modern science has clarified that this demon does not break the laws; rather, it pays for its sorting by using information. The demon measures a system, gains knowledge, and uses that knowledge to extract work. This process creates a flow of information, driven by a force similar to voltage in an electrical circuit. For decades, theorists have predicted that this flow of information should follow a simple rule, much like Ohm's law, which states that electrical current is proportional to voltage. However, proving this relationship in a real experiment has been incredibly difficult because it requires tracking microscopic changes in complex systems with extreme precision.

A team of researchers has now successfully demonstrated this relationship using a unique physical system: magnetic skyrmions. These are tiny, swirling magnetic structures, about one to two micrometers in diameter, that form in thin magnetic films. Unlike solid particles, skyrmions do not involve the movement of matter; instead, they are patterns of magnetism that can move and interact. At room temperature, these skyrmions jitter randomly due to thermal energy, a behavior known as Brownian motion. The researchers created a device with two parallel wires, each holding a single skyrmion. One skyrmion acts as the "demon," and the other acts as the "system." Both are confined to small rectangular areas where they can exist in one of two positions: top or bottom. The researchers used a microscope to watch the system skyrmion and applied a current to the wire holding the demon skyrmion. This current acted as a feedback mechanism: when the demon moved to a specific position, the researchers adjusted the current to encourage the system skyrmion to move in a desired direction. In this feedback cycle, no external force is directly applied to the system skyrmion; instead, the demon uses information about the system's state to guide its motion, effectively converting information into physical movement.

The experiment revealed that the flow of information behaves remarkably like an electrical current. As the researchers increased the strength of the feedback signal, the flow of information increased in direct proportion. This linear relationship confirmed that information transport follows a rule analogous to Ohm's law, where the "information current" is driven by an "information affinity," a force generated by the demon's knowledge. The researchers measured this flow by counting how often the skyrmions switched positions in a clockwise versus counter-clockwise direction. They found that the feedback created a steady, one-way flow of information around a loop, just as a battery drives current around a wire. Furthermore, they discovered that this flow is not perfectly smooth; it encounters resistance and scattering, similar to how electrons bump into atoms in a wire. To accurately describe the system, the team had to modify the standard laws of circuit theory. They found that the sum of forces around the loop is not zero, as it would be in a simple electrical circuit, because the demon's feedback introduces a non-conservative force that cannot be described by a simple potential.

The study also quantified the energy efficiency of this process. The researchers determined that the interaction between the two skyrmions creates a natural bias in the system, which they measured as an energy cost of about 0.47 times the thermal energy at room temperature. This value matched their theoretical predictions, confirming that the information flow is driven by the interplay between the demon's feedback and the natural repulsion between the skyrmions. By analyzing the data, the team calculated a value for "information conductance," which describes how easily information flows through the system. This value agreed with theoretical calculations derived from the rates at which the skyrmions jump between positions. The results show that while information circuits can be modeled using familiar electrical principles, they require adjustments to account for the unique way information carriers interact and scatter. This work provides the first experimental proof that information currents obey a linear response law, bridging the gap between abstract theory and physical reality. It suggests that future computing devices could be designed to harness these principles, potentially leading to computers that operate with the minimal energy cost dictated by the laws of thermodynamics.

Technical Summary: Ohm's Law for Information Revealed by a Skyrmion

Problem Statement
The reduction of energy costs in computation is a critical challenge in the era of artificial intelligence. While information thermodynamics has theoretically established that information transport follows linear response relationships analogous to electrical circuits—specifically that an "information current" is driven by a conjugate "information affinity" (analogous to voltage)—experimental verification of an Ohm-like constitutive relation for information has remained elusive. Existing theoretical frameworks, such as the Horowitz–Esposito (HE) formalism, predict that information circuits should obey laws similar to Ohm's law and Kirchhoff's laws. However, validating these predictions experimentally is difficult due to the requirement for detecting microscopic states in many-body systems, real-time feedback control, and the observation of vast numbers of stochastic events.

Methodology
To overcome these experimental hurdles, the authors constructed an information engine utilizing magnetic skyrmions. Skyrmions are topologically protected, particle-like magnetic structures (1–2 μm in diameter) that exhibit Brownian motion at room temperature without material transport. The experimental setup consists of a ferromagnetic thin film containing two adjacent rectangular potential wells:

The "Demon": A skyrmion in the left wire, whose motion is controlled by an applied current to provide feedback.
The "System": A skyrmion in the right wire, whose dynamics are observed but not directly forced.

The system is treated as a bipartite system where the positions of the two skyrmions define four discrete states (vertices I, II, III, IV) in a state space. The skyrmions interact via repulsive forces, creating an energy landscape where diagonal configurations (II and IV) are energetically stable. The researchers employed a magneto-optical microscope to continuously monitor the skyrmion positions and applied a nominal feedback current to the demon's wire. This current modulates the transition rates between states, creating a closed loop of transitions (I→II→III→IV→I). By analyzing the transition rates ( $W$ ) and state probabilities ( $p$ ), the authors calculated the information current ( $J$ ) and information affinity ( $F_{Info}$ ) for the system.

Key Contributions and Results
The study provides the first experimental realization of an Ohm-like constitutive relation for information transport in a magnetic skyrmion system. The key findings include:

Verification of Information Ohm's Law: The researchers demonstrated a linear relationship between the information current $J(C)$ and the information affinity $F_{Sys}^{Info}$ over a specific range ( $|F_{Sys}^{Info}| < 0.3 k_B$ ). The slope of this relationship yields the "information conductance" ( $L_{Sys}^{Info}$ ), which corresponds to electrical conductivity. The experimentally derived conductance ( $0.047/k_B$ ) aligns with theoretical predictions derived from transition rates ( $0.055 \pm 0.025/k_B$ ) and estimates based on the Einstein-Helfand relation.
Role of Scattering and Interactions: The linear response deviates when scattering of the information flow is neglected. The authors introduce a scattering parameter ( $\alpha$ ), determined to be 0.33, which is necessary to reconcile the theoretical model with experimental data. This indicates that in real information circuits, interactions between carriers and scattering effects must be accounted for.
Modification of Kirchhoff's Laws: The study clarifies that while the sum of information affinities in a closed loop is generally zero, the presence of Maxwell's demon (feedback) introduces a non-conservative affinity. Consequently, Kirchhoff's voltage law must be modified to include the feedback contribution ( $\sum F_{Loop} = \sum F_{Bare,FB}$ ). Additionally, the presence of scattering requires further modification to the affinity summation in the loop equation.
Saturation Effects: At high information affinities ( $|F_{Sys}^{Info}| > 5 k_B$ ), the linear relationship breaks down as the probability current saturates due to the probability distribution approaching 0.5.

Significance
The paper establishes that information transport in a physical system driven by Maxwell's demon obeys a linear response relationship analogous to Ohm's law, provided that interactions and scattering are properly modeled. By experimentally verifying the existence of information conductance and the modified Kirchhoff's laws, the authors demonstrate that information circuits can be treated with the same analytical framework as electrical circuits. This work bridges the gap between non-equilibrium statistical mechanics and information thermodynamics, providing a foundational step toward the design of energy-efficient computational devices that incorporate Maxwell's demon principles and the analysis of complex artificial intelligence and network systems.

Technical Summary: Ohm's Law for Information Revealed by a Skyrmion

More like this