Leveraging Environmental Correlations: The Thermodynamics of Requisite Variety

Abstract

Key to biological success, the requisite variety that confronts an adaptive organism is the set of detectable, accessible, and controllable states in its environment. We analyze its role in the thermodynamic functioning of information ratchets-a form of autonomous Maxwellian Demon capable of exploiting fluctuations in an external information reservoir to harvest useful work from a thermal bath. This establishes a quantitative paradigm for understanding how adaptive agents leverage structured thermal environments for their own thermodynamic benefit. General ratchets behave as memoryful communication channels, interacting with their environment sequentially and storing results to an output. The bulk of thermal ratchets analyzed to date, however, assume memoryless environments that generate input signals without temporal correlations. Employing computational mechanics and a new information-processing Second Law of Thermodynamics (IPSL) we remove these restrictions, analyzing general finite-state ratchets interacting with structured environments that generate correlated input signals. On the one hand, we demonstrate that a ratchet need not have memory to exploit an uncorrelated environment. On the other, and more appropriate to biological adaptation, we show that a ratchet must have memory to most effectively leverage structure and correlation in its environment. The lesson is that to optimally harvest work a ratchet's memory must reflect the input generator's memory. Finally, we investigate achieving the IPSL bounds on the amount of work a ratchet can extract from its environment, discovering that finite-state, optimal ratchets are unable to reach these bounds. In contrast, we show that infinite-state ratchets can go well beyond these bounds by utilizing their own infinite "negentropy". We conclude with an outline of the collective thermodynamics of information-ratchet swarms.

Thermodynamics of complexity and pattern manipulation

“…One thus can think of a tape with a pattern as one thinks of a rising weight (or any other form of battery) and treat it as an information reservoir [9,[12][13][14][15][16]. This approach has been used recently as a bridge from computational mechanics to modern thermodynamics [17][18][19].…”

“…In this context, a pattern may be treated as an information reservoir a source of free energy encoded in correlations (e.g. [9,[12][13][14][15][16][17][18][19]). Pattern manipulators, which convert a pattern to useful work or vice versa, are thus a type of heat engine.…”

“…One thus can think of a tape with a pattern as one thinks of a rising weight (or any other form of battery) and treat it as an information reservoir [9,[12][13][14][15][16]. This approach has been used recently as a bridge from computational mechanics to modern thermodynamics [17][18][19].The quantitative link between information, entropy and heat dissipation is given by Landauer's principle [11]: the minimum work cost of any information-processing task is proportional to the total change in information entropy 1 (just like macroscopic thermodynamics, where the minimum work required to slowly change between two states of the same internal energy is proportional to the change in thermodynamic entropy).Landauer's principle sets a lower bound on the work cost of performing an information processing task. In this article, we shall take Landauer's principle as our starting point.…”

Thermodynamics of Modularity: Structural Costs Beyond the Landauer Bound

“…This makes immediate intuitive sense since, by design, such transducers can anticipate the next input and adapt accordingly. This observation also emphasizes the principle that thermodynamic agents should requisitely match the structural complexity of their environment to leverage those informational correlations as a thermodynamic fuel [23]. We illustrate this result in the case of the golden mean pattern in Fig.…”

“…Section IV applies this analysis to information engines, an active subfield within the thermodynamics of computation in which information effectively acts as the fuel for driving physically embedded information processing [20][21][22][23][24]. The particular implementations of interestinformation ratchets-process an input symbol string by interacting with each symbol in order, sequentially transforming it into an output symbol string, as shown in Fig.…”