The computer is a tool for clear thinking: from unthinkable simulations to a deeper insight into heat transport

Up to about a decade ago, first-principles molecular dynamics was deemed at odds with the Green–Kubo linear-response theory of heat transport, because the partition of a system’s total energy into atomic contributions—until then routinely adopted to define the heat flux—lacks a well-defined quantum-mechanical analogue. In this talk, I will report on the journey that led from the removal of this stumbling block to a deeper insight into the theory of transport. The outset was marked by the realization that this difficulty actually affects classical no less than quantum-mechanical simulations—the partition of the total energy into local contributions, necessary for the definition of the energy flux, is intrinsically ill-defined in both cases. Key steps along the way were the formulation of two newly established principles—gauge and convective invariance—which ultimately led to the conclusion that any two local energy partitions (gauges) yielding the same atomic forces also result in the same heat conductivity, as expected on purely physical grounds. This conclusion, besides resolving the long-standing issue with first-principles simulations, is particularly relevant when simulating heat transport with neural-network potentials that, despite yielding the same forces by construction, are known to produce energy fluxes that depend on the model.