Thermodynamic Linear Algebra

Thermodynamic Linear Algebra proposes using classical thermodynamics as a near-term route to accelerating linear algebra, which underpins many modern engineering, science, and machine learning algorithms. The authors connect linear algebra problems to sampling from the thermodynamic equilibrium distribution of a system of coupled harmonic oscillators. They present thermodynamic algorithms for solving linear systems, computing matrix inverses and determinants, and solving Lyapunov equations. Under reasonable assumptions, they rigorously establish asymptotic speedups over digital methods that scale linearly in matrix dimension.