Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Maxwell's Thermodynamic Relations

Maxwell's Thermodynamic Relations

Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...

Thermodynamic Potentials

Thermodynamic Potentials

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...

The Carnot Cycle

The Carnot Cycle

Converting work to heat is an irreversible process, and the purpose of a heat engine is to reverse the effect partially. Heat engines aim to increase the efficiency of the reversal, that is, maximize the work retrieved from heat. If the efficiency of a heat engine were 100%, it would imply reversing the process completely without introducing any other effect. Thus, it would violate the second law of thermodynamics.
What could be the theoretical limit to the efficiency of a heat engine? The...

Thermodynamic Systems

Thermodynamic Systems

A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
Consider an example of tea boiling in a kettle. The...

Path Between Thermodynamics States

Path Between Thermodynamics States

Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:

Derivatives: Problem Solving

Derivatives: Problem Solving

Temperature-Dependent Growth of Brook TroutThe growth of brook trout is closely influenced by water temperature. Experimental data demonstrate how trout weight changes over a 24-day period in response to varying water temperatures. At lower temperatures, such as 15.5 degrees Celsius, brook trout show significant weight gain. However, as the temperature increases, the amount of weight gained steadily decreases. At the highest temperature measured, 24.4 degrees Celsius, trout experience a net...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Impact of solvent forces and broken symmetry on the assembly of designed proteins at a liquid-solid interface.

Nature communications·2026

Same author

Nonlinear thermodynamic computing out of equilibrium.

Nature communications·2026

Same author

Using the Metropolis algorithm to explore the loss surface of a recurrent neural network.

The Journal of chemical physics·2024

Same author

Learning protocols for the fast and efficient control of active matter.

Nature communications·2024

Same author

On the origin of cooperativity effects in the formation of self-assembled molecular networks at the liquid/solid interface.

Chemical science·2024

Same author

Learning stochastic dynamics and predicting emergent behavior using transformers.

Nature communications·2024

Same journal

Chemotactic self-organization captures the dynamics of mammalian hair follicle patterning.

Proceedings of the National Academy of Sciences of the United States of America·2026

Same journal

Tomographic imaging of superconducting order using particle-hole interference.

Proceedings of the National Academy of Sciences of the United States of America·2026

Same journal

Inhibitory potential of autologous neutralizing antibodies sets quantitative limits on the rebound-competent HIV-1 reservoir.

Proceedings of the National Academy of Sciences of the United States of America·2026

Same journal

Inferring epidemiological parameters under an infectious phylogeography model with visitor dynamics.

Proceedings of the National Academy of Sciences of the United States of America·2026

Same journal

Analytical modeling for suction cup designs for skin-interfaced wearable devices.

Proceedings of the National Academy of Sciences of the United States of America·2026

Same journal

Improving cell-free metabolism through direct integration of artificial respiratory chains.

Proceedings of the National Academy of Sciences of the United States of America·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Apr 5, 2026

A Gusseted Thermogradient Table to Control Soil Temperatures for Evaluating Plant Growth and Monitoring Soil Processes

A Gusseted Thermogradient Table to Control Soil Temperatures for Evaluating Plant Growth and Monitoring Soil Processes

Published on: October 22, 2016

Training thermodynamic computers by gradient descent.

Stephen Whitelam¹

¹Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720.

Proceedings of the National Academy of Sciences of the United States of America

|April 3, 2026

Summary

This summary is machine-generated.

Gradient descent training enables thermodynamic computers to perform computations like neural networks. This method achieves significant energy savings, potentially exceeding seven orders of magnitude for image classification tasks.

Keywords:

machine learning statistical mechanics thermodynamic computing

More Related Videos

Deep Neural Networks for Image-Based Dietary Assessment

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

Related Experiment Videos

Last Updated: Apr 5, 2026

A Gusseted Thermogradient Table to Control Soil Temperatures for Evaluating Plant Growth and Monitoring Soil Processes

A Gusseted Thermogradient Table to Control Soil Temperatures for Evaluating Plant Growth and Monitoring Soil Processes

Published on: October 22, 2016

Deep Neural Networks for Image-Based Dietary Assessment

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

Area of Science:

Thermodynamic computing
Machine learning
Computational physics

Background:

Thermodynamic computing offers potential energy efficiency advantages over digital computation.
Training thermodynamic computers for specific tasks remains a significant challenge.

Purpose of the Study:

To develop a gradient descent-based training method for thermodynamic computers.
To enable thermodynamic computers to perform desired computations, analogous to neural networks.
To quantify the energy efficiency of trained thermodynamic computers.

Main Methods:

A teacher-student training scheme was employed within a digital simulation.
Gradient descent was used to adjust thermodynamic computer parameters by maximizing trajectory probability.
An idealized trajectory, based on a trained neural network, guided the thermodynamic computer's training.
The method was demonstrated on an image-classification task.

Main Results:

The trained thermodynamic computer successfully performed computations analogous to the neural network.
The energy cost ratio (thermodynamic vs. digital) exceeded seven orders of magnitude for image classification.
Gradient descent was established as a viable training methodology for thermodynamic computing.

Conclusions:

Gradient descent is a powerful tool for training thermodynamic computers.
Thermodynamic computing, trained via machine learning principles, offers substantial energy advantages.
This work bridges machine learning and thermodynamic computing, paving the way for energy-efficient computation.