Thermodynamic cost of computing: from logic circuits to RASP

Stochastic thermodynamics extends equilibrium statistical physics to systems arbitrarily far from thermal equilibrium, with arbitrarily many quickly evolving degrees of freedom. These features make it the correct framework for analyzing the thermodynamics of real-world computers. Moreover, recently stochastic thermodynamics has been used to prove that the ``mismatch cost'' of a dynamic process is a lower bound on the energy dissipation (``entropy production'') of any physical system that implements that process, regardless of the physical details of the system. So mismatch cost can be used to lower bound the entropy production of any computation, regardless of the physical details of the system used to implement that computation. Here we first, show that mismatch cost may be significant on the macroscopic scale, not just on the nano-scale (in contrast to many other stochastic thermodynamics bounds). We also show that coarse-graining a system in time and and / or space changes the mismatch cost, but that cost still provides lower bounds to the microscopic entropy production of running the system. We then argue that traditional computer science measures of algorithmic efficiency, focused on the resource costs of ``space'' and ``time'' complexity, should include a third resource cost - thermodynamic cost - and that mismatch cost is well-suited to bounding such cost for arbitrary computational machines. Accordingly, we derive the mismatch cost for running an arbitrary Random Access Stored Program machine (a simplified model of a microprocessor).