  We develop a physics-based model for classical computation based on
autonomous quantum thermal machines. These machines consist of few interacting
quantum bits (qubits) connected to several environments at different
temperatures. Heat flows through the machine are here exploited for computing.
The process starts by setting the temperatures of the environments according to
the logical input. The machine evolves, eventually reaching a non-equilibrium
steady state, from which the output of the computation can be determined via
the temperature of an auxilliary finite-size reservoir. Such a machine, which
we term a "thermodynamic neuron", can implement any linearly-separable
function, and we discuss explicitly the cases of NOT, 3-majority and NOR gates.
In turn, we show that a network of thermodynamic neurons can perform any
desired function. We discuss the close connection between our model and
artificial neurons (perceptrons), and argue that our model provides an
alternative physics-based analogue implementation of neural networks, and more
generally a platform for thermodynamic computing.
