Information and energy exchange – on Maxwell’s demon

Maxwell’s demon

Maxwell’s demon is a thought experiment proposed by 19th century physicist James Clerk Maxwell, which has become a widely recognised challenge to the second law of thermodynamics.

Maxwell placed a partition separating two rooms in a container and placed an imaginary entity called a ‘demon’ in the partition. This demon observes the movement of the molecules and sorts them according to certain rules. For example, the demon is assumed to be able to move fast molecules into one room and slow molecules into the other. In this way, the slow molecules will gather in the low-energy room and the fast molecules in the high-energy room, resulting in a temperature difference and energy being concentrated in one of them. This process appears to reverse the ‘natural diffusion’ of energy and thus seems to violate the second law of thermodynamics (the law of increasing entropy).

According to the second law of thermodynamics, entropy (the degree of disorder) increases in closed systems and the distribution of energy tends to equalise. Maxwell’s demon was the subject of subsequent controversy because it appeared to be a violation of this law.

In response to this thought experiment, physicists at the beginning of the 20th century argued as follows

• Information theory perspective: in order for Maxwell’s demon to sort out molecules, it needs to ‘observe’ their states of motion and use this information to move them. In practice, the processing of this information requires energy, and the energy consumption to obtain the information compensates for the energy loss associated with the demon’s operation. It is therefore concluded that the second law of thermodynamics is not broken by the demon ‘wasting’ energy.
• Boltzmann’s entropy theory: Ludwig Boltzmann considered entropy to have a stochastic nature and stressed that the second law of thermodynamics is a statistical law that cannot be ignored as a ‘physical process’. It was held that the processing of information consumes energy and that ‘sorting operations’, such as those performed by demons, do not avoid increasing entropy.

Today, Maxwell’s demon is seen as a physics ‘paradox’ or thought experiment, and an important tool for understanding the relationship between energy and information. In particular, the study of the exchange of information and energy became an important topic in quantum information theory and computational theory.

Exchange of information and energy

The exchange of information and energy, which was at the centre of the debate in Maxwell’s demon, has become an important concept in physics and information theory, as well as in biology and artificial intelligence. They are often closely interrelated and affect the efficiency of physical processes and information processing. Invisible information is seen as energy, and these are closely related to physics, chemistry and biological brocesses.

1. the relationship between information and energy in physics: information and energy are closely related in the following contexts, especially in the context of thermodynamics and quantum mechanics.

(1) Thermodynamics and energy costs: according to Landauer’s Principle, the erasure of information requires energy, and the entropy increase associated with this process serves to protect the second law of thermodynamics, which states that information processing involves a physical energy cost. According to this principle, a minimum of (kT ln 2) energy (thermal energy) is required to erase one bit of information ((k) is Boltzmann’s constant and (T) is absolute temperature). The heat generated when computers and processors perform calculations is a form of this information processing energy.

(2) Entropy of information: thermodynamic entropy and information entropy (Shannon entropy) are similar. In the process of increasing entropy, information tends to lose order and dissipate energy.

(3) Maxwell’s demon: the virtual entity ‘Maxwell’s demon’ was supposed to be able to use information to control the flow of energy and reduce entropy. However, according to Landauer’s principle, the processing of information itself entails an energy cost, so it is considered impossible for a demon-like entity to break the law of conservation of energy.

2. exchange of information and energy in biology: life is founded on the integration of information processing (e.g. DNA transcription, protein synthesis) and energy conversion (e.g. respiration, photosynthesis).

(1) DNA and energy: DNA stores information and directs the traits and metabolic activities of an organism. ATP (energy molecules) is used for the replication and expression of this information.

(2) Networks and feedback: in neural networks and metabolic pathways, information flow (signalling) is directly linked to energy (ATP consumption). For example, the transmission of neural signals requires energy to maintain the membrane potential.

3. information science and energy efficiency: energy efficiency is becoming an increasingly important issue as information technology evolves.

(1) Energy efficiency of computers: transistor and processor design is required to reduce energy consumption per information process. Quantum computing will be one of the areas where energy efficiency is expected to improve.

(2) Information compression and energy: efficient compression of information can reduce the energy required for communication and storage.

(3) Machine learning and energy: the training of deep learning and AI models, as discussed in ‘Deep learning’, requires a huge amount of energy, but efficiency is being improved by optimising information processing algorithms.

The relationship between this information and energy, and the technology to control their exchange (e.g. efficiency), could lead to progress in a number of areas, as described below.

• Energy-efficient communication: 5G and future communication technologies aim to convey more information while reducing energy consumption.
• Information-driven energy management: smart grids described in “Electricity storage technology, smart grids and GNNs” will utilise sensors and AI to optimise energy consumption.
• Integration of information processing and life: new bio-inspired technologies could emerge by mimicking the information processing and energy conversion mechanisms of living organisms.

It can be argued that the exchange of information and energy is a key theme at the intersection of physics, life, information science and artificial intelligence, and is key to future technological innovation.

AI technologies in terms of information and energy exchange

AI technologies are considered from the perspective of information and energy exchange. They can be considered from three aspects: efficiency of information processing, reduction of energy consumption and optimisation of design based on the laws of nature. They are discussed below.

1. energy costs of information processing in AI: In AI technology, large-scale data processing and training of models consume enormous amounts of energy. This energy consumption is a fundamental issue in information processing.

(1) Deep learning and energy:

• Energy load of training: training deep learning models (e.g. GPT and BERT) requires hundreds of thousands to millions of GPU hours and consumes large amounts of energy; on supercomputers used by organisations such as OpenAI, the training process consumes several hundred megawatts hours (MWh) or more of power may be consumed.
• Energy efficiency of inference: the actual inference process using AI models depends on the model size and the efficiency of the algorithm, and lighter models (e.g. DistilBERT) can reduce energy consumption.

(2) Integration with quantum computing.

• Quantum computing, described e.g. in ‘Quantum Mechanics, Artificial Intelligence and Natural Language Processing’, has the potential to be more energy efficient than conventional computing techniques; it is expected that AI algorithms can be adapted to quantum computing to further optimise the training and inference process.

2. information and energy efficiency optimisation technologies for AI

(1) Algorithm optimisation

• Use of sparse models: sparse models, as described in ‘Machine learning with sparsity’, improve the efficiency of information processing and reduce energy consumption by reducing unnecessary parameters in the model. For example, sparse networks (Sparse Neural Networks) can maintain high accuracy while using less memory and computational resources.
• Compression techniques: techniques such as model quantisation (Quantisation) and knowledge distillation (Knowledge Distillation), described in ‘On lightweighting models through pruning, quantisation, etc.’, can be used to reduce model size and improve energy efficiency during inference. (2) Joint hardware and AI.

(2) Hardware and AI co-design

• Edge AI devices: when running AI in edge environments such as smartphones and IoT devices as described in ‘Sensor data & IOT technologies’, dedicated hardware (e.g. Google TPU, NVIDIA Jetson) as described in ‘Thinking Machines Machine learning and its hardware implementation’ can be used, NVIDIA Jetson) can significantly improve energy efficiency.
• Neuromorphic computing: computational architectures that mimic the human brain are highly energy efficient. Spike neural networks (SNN) can be employed to enable real-time processing while saving energy.

3. designing AI from nature: to optimise the exchange of information and energy, it is important to mimic the efficient information processing and energy conversion mechanisms in nature, as described in ‘Soft machines and biocomputers’.

(1) Energy-efficient biological systems

• Brain modelling: the human brain performs complex information processing using as little as 20 W of energy. AI design is underway to mimic this, and DeepMind research is developing reinforcement learning algorithms that refer to the neural activity of the brain.

(2) Self-organisation and energy efficiency

• In nature, efficient information exchange takes place through distributed networks (e.g. bird flocks, ant nests) with self-organisation capabilities, as described in ‘Considerations on the technologies needed to build autonomous artificial intelligence’. By mimicking this mechanism, decentralised AI systems can be built in an energy-efficient manner.

Examples of applications of information and energy exchange technologies include

• Smart energy systems: a smart grid as described in ‘Power storage technology, smart grids and GNNs’ that utilises AI to optimise energy demand and supply in real time can be realised. Energy efficiency can be increased through information processing.
• Sustainable AI: In the research community, the realisation of ‘green AI’ to reduce energy consumption has been proposed. This not only seeks to improve AI performance, but also efficient energy utilisation.
• Low-energy AI applications: in energy-constrained environments (e.g. space exploration, remote sensing), AI systems that combine information processing and energy efficiency are essential and are being explored for these.

From the perspective of information and energy exchange technologies, the energy consumption of large-scale AI models is a concern from a sustainability perspective, and the compatibility between information processing efficiency and energy consumption reduction is an urgent issue. In response to them, design that takes into account the exchange of information and energy is considered to be the key to opening up new possibilities for AI technology. As an approach to this end, bio-inspired AI that incorporates natural mechanisms and integration with new physical paradigms (e.g. quantum computing) is expected.

reference book

Reference books on Maxwell’s demon and AI technology in relation to the exchange of information and energy are described below.

1. Maxwell’s Demon and AI technology.

*Maxwell’s Demon: Entropy, Information, Computing
Author(s): Harvey Leff, Andrew Rex
Abstract: This book delves deeply into the relationship between the concept of Maxwell’s Demon and information and computational theory.

Information Theory and Statistical Mechanics
Author: E.T. Jaynes
Abstract: A fundamental reference on the interface between information theory and thermodynamics.

Deep Learning for Physical Sciences
Author: Carlo Cafaro
Abstract: Describes methods for applying AI to physics and thermodynamic systems.

Artificial Intelligence and Thermodynamics: A New Frontier
Author: multi-authored collection of papers
Abstract: Documents the latest research on the integration of AI and thermodynamics.

2. energy efficiency and AI technologies
– ‘Efficient Processing of Deep Neural Networks: A Tutorial and Survey’
Vivienne Sze, et al.
– Resource covering the fundamentals and applications of efficient design and implementation of AI models.

– ‘Energy-Efficient Computing & Data Centres’
Samee U. Khan, et al.
– Details strategies for energy efficiency in data centres and AI training.

– ‘Green AI-Powered Intelligent Systems for Disease Prognosis’.

3. algorithm design and information processing
– Deep Learning (Adaptive Computation and Machine Learning Series).
Ian Goodfellow, Yoshua Bengio, Aaron Courville
– Covers basic and advanced topics in deep learning. Also covers energy efficient learning methods.

– ‘Neural Networks and Deep Learning: A Textbook’
Charu C. Aggarwal.
– Features algorithm design that takes into account the relationship between information processing and energy consumption.

– ‘Sparse Modelling: Theory, Algorithms, and Applications’
Irina Rish, Genady Chryssostomidis
– Covers the theory and applications of sparse modelling and efficient information representation in AI.

4. integration of hardware and AI
– ‘Neuromorphic Computing and Beyond: Principles and Applications’
World Scientific Publishing
– Comprehensive coverage of the theory and applications of neuromorphic computing.

– ‘Computer Architecture: A Quantitative Approach’
John L. Hennessy, David A. Patterson
– On the design of hardware efficiency and information processing architecture in AI systems.

– 「Artificial Intelligence Hardware Design: Challenges and Solutions」

5. nature-inspired approaches.
– ‘Biologically Inspired Artificial Intelligence for Computer Games’.
D. P. Davis.
– Theory and Implementation of Biologically Inspired AI Design.

– ‘The Nature of Computation’
Cristopher Moore, Stephan Mertens
– A book on the nature of computation and information processing in nature.

– ‘Self-Organisation in Biological Systems’
Scott Camazine, et al.
– Learn the principles of self-organisation and distributed information processing, with applications to AI.

6. academic papers and current resources
– ‘Energy Efficiency of Neural Network Training’

– ‘The Review of Green Artificial Intelligence’
Source: various Journals
– Review of papers focusing on sustainable implementation of AI.