Nonlinear thermodynamic computing out of equilibrium

We present the design for a thermodynamic computer that can perform arbitrary nonlinear calculations in or out of equilibrium. Simple thermodynamic circuits, fluctuating degrees of freedom in contact with a thermal bath and confined by a quartic potential, display an activity that is a nonlinear function of their input. Such circuits can therefore be regarded as thermodynamic neurons, and can serve as the building blocks of networked structures that act as thermodynamic neural networks, universal function approximators whose operation is powered by thermal fluctuations. We simulate a digital model of a thermodynamic neural network, and show that its parameters can be adjusted by genetic algorithm to perform nonlinear calculations at specified observation times, regardless of whether the system has attained thermal equilibrium. This work expands the field of thermodynamic computing beyond the regime of thermal equilibrium, enabling fully nonlinear computations, analogous to those performed by classical neural networks, at specified observation times.

💡 Research Summary

The paper introduces a novel framework for performing arbitrary nonlinear computations using thermodynamic systems that need not reach equilibrium. Traditional thermodynamic computing relies on the Boltzmann distribution of a system at thermal equilibrium; calculations such as matrix inversion are encoded in equilibrium correlation functions, which imposes two major constraints: (i) the system must be allowed to equilibrate, often requiring long and unpredictable timescales, and (ii) only a limited class of problems (e.g., those representable by a positive‑definite matrix) can be mapped onto an equilibrium distribution.
To overcome these limitations, the authors propose “thermodynamic neurons” built from a single scalar degree of freedom (x) confined by a quartic potential
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