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

Abstract

Replication can be envisaged as a computational process that is able to generate and maintain order far-from-equilibrium. Replication processes, can self-regulate, as the drive to replicate can counter degradation processes that impact on a system. The capability of replicated structures to access high quality energy and eject disorder allows Landauer's principle, in conjunction with Algorithmic Information Theory, to quantify the entropy requirements to maintain a system far-from-equilibrium. Using Landauer's principle, where destabilising processes, operating under the second law of thermodynamics, change the information content or the algorithmic entropy of a system by ΔH bits, replication processes can access order, eject disorder, and counter the change without outside interventions. Both diversity in replicated structures, and the coupling of different replicated systems, increase the ability of the system (or systems) to self-regulate in a changing environment as adaptation processes select those structures that use resources more efficiently. At the level of the structure, as selection processes minimise the information loss, the irreversibility is minimised. While each structure that emerges can be said to be more entropically efficient, as such replicating structures proliferate, the dissipation of the system as a whole is higher than would be the case for inert or simpler structures. While a detailed application to most real systems would be difficult, the approach may well be useful in understanding incremental changes to real systems and provide broad descriptions of system behaviour.

The information requirements of complex biological and economic systems with algorithmic information theory

“…The algorithmic entropy aligns with the Shannon entropy and the entropy of thermodynamics [2,7,8]. Whenever pattern or structure is observed in a string defining a natural system, an algorithm can be constructed to provide a compressed description of the string, although unrecognised structure may allow further compression.…”

“…This measure is similar to the Gács entropy, Kolmogorov's Algorithmic Minimum Sufficient Statistic and Zureks intuitive physical entropy concept [2]. The entropy of Shannon's information theory, by contrast, is a characteristic of the macrostate itself and corresponds to H(Shannon) = log 2 Ω.…”

“…But, as is discussed further in Section 2, information differences are independent of the UTM used. The flow of information (converted to bits) passing through a real world computation is the same as the laboratory simulation [2]. As a consequence, if H(s) is the number of programme bits to describe the system, and H(equil) is the number of bits to describe its disordered local equilibrium, the degree of order is H(equil) -H(s).…”

“…If there are Ω microstates in the macrostate, a particular microstate, can be specified by a two-stage algorithm. The first identifies the particular microstate in the macrostate and has length log 2 Ω bits, while the second defines the characteristics of the set of allowable microstates [2,18]. The information content that is common to each microstate in the macrostate is called the provisional entropy H prov and is given by [18]:…”

“…Importantly, when appropriately coded, the number of bits defines the algorithmic entropy that is related to the traditional entropies. AIT has been used to track the emergence of order in biological systems [2], but conceptual issues need to be explored to effectively apply the approach more widely.…”