Writing, Proofreading and Editing in Information Theory

Abstract

Information is a physical entity amenable to be described by an abstract theory. The concepts associated with the creation and post-processing of the information have not, however, been mathematically established, despite being broadly used in many fields of knowledge. Here, inspired by how information is managed in biomolecular systems, we introduce writing, entailing any bit string generation, and revision, as comprising proofreading and editing, in information chains. Our formalism expands the thermodynamic analysis of stochastic chains made up of material subunits to abstract strings of symbols. We introduce a non-Markovian treatment of operational rules over the symbols of the chain that parallels the physical interactions responsible for memory effects in material chains. Our theory underlies any communication system, ranging from human languages and computer science to gene evolution.

Fluctuation relations for irreversible emergence of information

“…Using the mutual information quantity, I − I (D) ≤ ∆U (D) − ∆U /T , which allows the information of the revised chain to be higher than that of the written chain (I > I (D) ) provided that the expected energy of the revised chain is lower than that of the written chain (∆U < ∆U (D) , necessary but not sufficient condition). Inequality ( 6) is reminiscent of an earlier result demonstrated independently 33 : by setting equal states for the written and revised chains, it is found that S − S (D) ≥ U −U (D) /T , which was used to formulate necessary and sufficient conditions for effective proofreading and editing in information theory 31 .…”

“…The chain has an associated reading direction, which is the one that makes the information along the chain meaningful (from left to right in Fig. 1), according to the language rules 31 . For example, a DNA template strand is copied (transcribed) from its 3' end to its 5' end during replication (transcription) and English language or sheet music are interpreted from left to right.…”

“…The construction of the chain is subjected to a protocol, λ , which stochastically drives its growth through privileged sequences. A general protocol combines two main actions: writing, which entails the incorporation of characters along the reading direction, and revision, which comprises the proofreading + editing of the characters 31 . More in depth, writing involves testing characters within the alphabet at each chain subunit in turn, allowing one to equilibrate with respect to the previously incorporated neighbors, and then moving on, freezing that character permanently; and revision entails a global equilibration of the chain, during which characters can fluctuate non-sequentially (within the alphabet values) at each chain subunit.…”

“…Due to their abstract nature, these theorems yield no specific insight into information theory, where time is not necessarily defined. Recent generalizations separate the role of information and feedback control 28,29 , but still the interpretation of non-Markovianity, irreversibility and reversibility in terms of purely informational operations such as reading, writing and error correction 30,31 remains obscured. In this regard, just by considering reversibility at the single sequence level and conservation laws, we next present two pairs of fluctuations equalities in the construction of information chains, which use depends on energy exchange constraints.…”

Microscopically Reversible Pathways with Memory

“…Complete memory effects have been considered in the study of spatial chains made up of physical subunits, including those with symbolic meaning, to access non-equilibrium dynamics [23] and information management in nanoscale systems [24]. They have also been taken into account to analyze abstract strings of symbols for the paradigm of communication [25]. However, full memory effects in temporal chains of events have never been treated from an exact perspective.…”