Algorithmic Entropy and Landauer’s Principle Link Microscopic System Behaviour to the Thermodynamic Entropy

Abstract

Algorithmic information theory in conjunction with Landauer’s principle can quantify the cost of maintaining a reversible real-world computational system distant from equilibrium. As computational bits are conserved in an isolated reversible system, bit flows can be used to track the way a highly improbable configuration trends toward a highly probable equilibrium configuration. In an isolated reversible system, all microstates within a thermodynamic macrostate have the same algorithmic entropy. However, from a thermodynamic perspective, when these bits primarily specify stored energy states, corresponding to a fluctuation from the most probable set of states, they represent “potential entropy”. However, these bits become “realised entropy” when, under the second law of thermodynamics, they become bits specifying the momentum degrees of freedom. The distance of a fluctuation from equilibrium is identified as the number of computational bits that move from stored energy states to momentum states to define a highly probable or typical equilibrium state. When reversibility applies, from Landauer’s principle, it costs k B l n 2 T Joules to move a bit within the system from stored energy states to the momentum states.