Thermodynamic Networks: Harnessing Non-Equilibrium Steady States for Computation

TL;DR

This paper introduces thermodynamic networks that utilize non-equilibrium steady states for autonomous computation, demonstrating their ability to perform complex tasks like function approximation and digit classification.

Contribution

It establishes a theoretical framework linking non-equilibrium steady states with computational expressivity, highlighting the role of Negative Differential Conductance (NDC) in enabling universal computation.

Findings

Networks with NDC can approximate any function.

Quantum dot and enzymatic networks with NDC perform well on benchmarks.

NDC is essential for non-monotonic computational capabilities.

Abstract

We introduce thermodynamic networks, a general framework for autonomous, physics-based computation using non-equilibrium steady states. These networks are modeled as a collection of finite-size reservoirs that exchange conserved quantities--such as electric charge or molecular number--while relaxing to a non-equilibrium steady state, which encodes the solution of a computational problem. We identify Negative Differential Conductance (NDC) as the critical physical property governing the computational expressivity of the thermodynamic network. While networks lacking NDC are restricted to computing monotonic functions, the presence of NDC enables universal function approximation. For the training of the network, we use protocols that take advantage of the natural tendency of the system to equilibrate. We illustrate the versatility of our approach via two different platforms: quantum dot networks and enzymatic reaction networks. Both systems can be engineered to have NDC, enabling high performance in standard benchmarks, including sine function approximation and MNIST digit classification. Overall, our work establishes a rigorous link between non-equilibrium steady states and computational expressivity.