Understanding how replication processes can maintain systems away from equilibrium using Algorithmic Information Theory

Foundations of algorithmic thermodynamics

Gács's coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given physical state. Unlike the Boltzmann and Gibbs-Shannon entropies, it requires no prior commitment to macrovariables or probabilistic ensembles, rendering it applicable to settings arbitrarily far from equilibrium. For measure-preserving dynamical systems equipped with a Markovian coarse graining, we prove a number of fluctuation inequalities. These include algorithmic versions of Jarzynski's equality, Landauer's principle, and the second law of thermodynamics. In general, the algorithmic entropy determines a system's actual capacity to do work from an individual state, whereas the Gibbs-Shannon entropy gives only the mean capacity to do work from a state ensemble that is known a priori.

Landauer's Principle a Consequence of Bit Flows, Given Stirling's Approximation

According to Landauer's principle, at least kBln2T Joules are needed to erase a bit that stores information in a thermodynamic system at temperature T. However, the arguments for the principle rely on a regime where the equipartition principle holds. This paper, by exploring a simple model of a thermodynamic system using algorithmic information theory, shows the energy cost of transferring a bit, or restoring the original state, is kBln2T Joules for a reversible system. The principle is a direct consequence of the statistics required to allocate energy between stored energy states and thermal states, and applies outside the validity of the equipartition principle. As the thermodynamic entropy of a system coincides with the algorithmic entropy of a typical state specifying the momentum degrees of freedom, it can quantify the thermodynamic requirements in terms of bit flows to maintain a system distant from the equilibrium set of states. The approach offers a simple conceptual understanding of entropy, while avoiding problems with the statistical mechanic's approach to the second law of thermodynamics. Furthermore, the classical articulation of the principle can be used to derive the low temperature heat capacities, and is consistent with the quantum version of the principle.

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

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.

An Economy Viewed as a Far-from-Equilibrium System from the Perspective of Algorithmic Information Theory

This paper, using Algorithmic Information Theory (AIT), argues that once energy resources are considered, an economy, like an ecology, requires continuous energy to be sustained in a homeostatic state away from the decayed state of its (local) thermodynamic equilibrium. AIT identifies how economic actions and natural laws create an ordered economy through what is seen as computations on a real world Universal Turing Machine (UTM) that can be simulated to within a constant on a laboratory UTM. The shortest, appropriately coded, programme to do this defines the system’s information or algorithmic entropy. The computational behaviour of many generations of primitive economic agents can create a more ordered and advanced economy, able to be specified by a relatively short algorithm. The approach allows information flows to be tracked in real-world computational processes where instructions carried in stored energy create order while ejecting disorder. Selection processes implement the Maximum Power Principle while the economy trends towards Maximum Entropy Production, as tools amplify human labour and interconnections create energy efficiency. The approach provides insights into how an advanced economy is a more ordered economy, and tools to investigate the concerns of the Bioeconomists over long term economic survival.