The Reformulated Law of Infodynamics
An organizing principle for the origin of life and other complex processes
Melvin Vopson and S. Lepadatu introduced the Second Law of Infodynamics (SLID) with the bold claim that it “has massive implications for future developments in genomic research, evolutionary biology, computing, big data, physics, and cosmology” [1]. Their proposed law states that while physical entropy increases in accordance with the Second Law of thermodynamics, a system’s information entropy tends to decline.
Entropy is commonly described as disorder, but disorder is in the eyes of the beholder. It is defined as an observer’s uncertainty of a system’s actual physical microstate, and it is not a physical property of state. Vopson and Lepadatu describe physical entropy as the uncertainty of a system’s actual microstate from among its non-information-bearing microstate possibilities, meaning, evidently, that they are objectively unknowable. Information entropy, in contrast, is based on information-bearing microstate possibilities, which are unknown, but definite and knowable.
Vopson and Lepadatu illustrated the principle by changes in the SARS Covid virus. Its information-bearing microstates are the many possible arrangments of the RNA’s four building blocks. The information entropy is the uncertainty of which arrangement is the RNA’s actual definite and measurable microstate.
Measurements of the virus between January 2020 and October 2021 showed a decline in the virus’s information entropy. The decline can be interpreted as an increase in its information content. As a virus evolves, it certainly does in some sense gain information, as evidenced by its evolving ability to evade antibodies and to manipulate its target genomes for its own reproduction.
Vopson and Lepadatu’s proposed law offers a governing principle of how complex systems process information. The law would provide deeper understanding of processes, from machine learning to the origin of life. However, they acknowledged important unresolved questions. First and foremost is the question of an observer’s role in defining physical states or processes. Although the Second Law of thermodynamics is an empirically validated and universally accepted, it is not a fundamental law of physics. Hamiltonian mechanics, which underlies classical and quantum physics, does not recognize entropy or any principle of irreversible change as fundamental. Second, the SLID, as formulated, is more of an empirical observation of information entropy decline than a formal law.
To establish the SLID as a well-defined principle of mechanics, I reformulate it within the framework of the thermocontextual interpretation (TCI) [2]. I previously proposed the TCI as a generalization of thermodynamics and mechanics within a single thermocontextual framework [3,4]. The TCI resolves some of the fundamental questions of physics, including: the nature of time, causality, quantum entanglement, nonlocality, and the spontaneous evolution of functional complexity [3−6].
The TCI generalizes Hamiltonian mechanics with the addition of three postulates:
Postulate 1. Temperature is a measurable property of state.
Postulate 2. Absolute zero temperature can never be reached.
Postulate 3. There are no hidden state variables.
The first two postulates provide the foundation for defining the thermocontextual state. They are based on the zeroth and third laws of thermodynamics, and they are accepted as empirical facts. The TCI first defines a system’s positive ambient temperature as the minimum temperature of the surroundings with which the system can interact. It defines exergy as a measure of energy’s value by its potential for work on the system’s ambient surroundings. The balance of energy is ambient heat, which has zero capacity for work. Thermal entropy is then defined as the ratio of ambient heat to ambient temperature and as a measure of ambient thermal randomness. Postulates One and Two extend the scope of mechanics by recognizing ambient temperature, exergy, and thermal entropy as fundamental and objective thermocontextual properties of the physical state.
Postulate Three explicitly rejects the possibility of hidden variables, which, by tautology, cannot be measured. With no hidden variables, a system’s physical state is observable, in principle, and this means that it is definite, whether observed or not. Postulate Three does not imply, however, that a system always exists as an observable state. A system that is not perfectly and completely observable does not exist as a state. Rather, it is in transition between states and unobservable.
The TCI’s also has two postulates of transitions, which are updated in my most recent article[2]:
Postulate 4 (Minimum Accessibility). A system’s accessible energy declines over time, and
Postulate 5 (Maximum Work). A transition tends to maximize its work output.
Postulate Four addresses the stability of states. A state of lower accessible energy (accessibility) is more stable than a state of higher accessibility. Accessibility describes the capacity for work on an observer’s fixed reference state. As water flows over a water wheel, for example, it approaches a more stable state of lower accessibility and capacity for work. The updated Postulate Four defines stability by accessibility rather than exergy, because exergy is defined with respect to the ambient surroundings, which might itself change during a transition. Postulate Four establishes the thermodynamic arrow of time for a fixed reference observer.
The TCI recognizes two special cases for Postulate Four. The first is the Second Law of thermodynamics, which describes the production of thermal entropy. This corresponds to the irreversible dissipation of exergy to ambient heat and declines in both exergy and accessible energy. The other special case is MaxEnt [7]. MaxEnt describes dispersion, such as the spontaneous mixing of ink and water. Dispersion increases the number of possible microstate configurations, and this increases the system’s mechanical disorder, which is the statistical entropy of mechanics. Dissipation and dispersion describe two distinct transitions to a more stable state. Each reduces a system’s accessible energy and is a special case of the more Postulate Four.
Whereas minimum accessibility describes the stability of states, Postulate Five addresses the stability of transitions. It states that the most stable transition is the one with the highest output of work. Postulate Five provides an essential counterbalance to Postulate Four. Dissipation and dispersion destroy accessible energy, but a transition tends to defer this by outputting as much accessible energy for work as possible (Postulate Five).
A special case of Postulate Five is the maximum efficiency principle (MaxEff). MaxEff describes nature’s empirical tendency to utilize energy as efficiently as possible [6,7]. One way to increase efficiency is to divert accessible energy to do work of creating and sustaining dissipative structures. Dissipative structures include thermal convection and whirlpools, which form spontaneously and are sustained by external inputs of heat or fluid. Dissipative structures also include the evolving biosphere, which is driven and sustained by the input of sunlight. MaxEff drives the arrow of increasing functional complexity.
Another special case of Postulate Five is the reformulated law of infodynamics (RLID) [2]. The RLID replaces information entropy of the SLID with the DKL information gap [8] between a system’s description and its actual physical microstate. A low information entropy is a measure of a state description’s precision, but a low information gap is a measure of the description’s accuracy. The RLID states that an observer has a spontaneous potential to reduce its information gap. The increased information provides the observer greater access to an open system’s energy output for work, and from Postulate Five, this increases the stability of energy flow through the system’s. The RLID states that, given an energy source, an external agent will narrow its information gap to find a way to utilize that energy.
The RLID explains the spontaneous change in the SARS-Covid virus’s information. The virus has the role of external agent and the virus’s target cells have the role of the virus’s energy source. The change in the virus’s RNA reflects the closing of its information gap with its target’s genome. Narrowing the information gap increases the virus’s access to its target’s energy. In the case of the virus, the narrowing information gap is achieved through random mutations and selection. The RLID provides a selection criterion for the virus to preserve mutations that enable it to access its target’s energy and to increase its work of reproduction.
The RLID provides the drive to create self-replicating chemical arrays of increasing length, energy, and information content. Figure 1 illustrates the assembly of a statistical array of ambient components by the addition of energy from an external source. The assembled array has positive energy, but if an observer-agent has zero information on it, it cannot access the energy, and the array has zero accessibility. The RLID provides an observer-agent with the drive to acquire information on the array, allowing it greater access to the array’s energy.
One way to reduce the agent’s information gap is to create a template that can catalyze the creation of a known sequence. Given a template and a procedure to use it, the template can replicate the array with a known sequence and zero information gap. This maximizes the array’s accessible energy. The origin of self-replicating templates is an essential step in the chemical origin of life, and it is a simple consequence of the RLID.
Postulate Four’s description of the relative stability of states introduces the concept of value to physics. Postulate Five’s description of the relative stability of processes introduces the concept of purpose. The TCI’s postulates apply to any system involving energy or any medium of value. Given its very general nature, Postulate Five and its corollaries, MaxEff and RLID, will likely have applications as an organizing principle for evolution within a wide range of complex physical, biological, or social systems.
- https://pubs.aip.org/aip/adv/article/12/7/075310/2819368/Second-law-of-information-dynamics
- The second law of infodynamics: a thermocontextual reformulation. https://www.preprints.org/manuscript/202410.1664/v1
- Time and Causality: a Thermocontextual Perspective. https://www.mdpi.com/1099-4300/23/12/1705
- https://medium.com/science-and-philosophy/a-thermocontextual-perspective-reimagining-physics-part-3-d95313ccd709
- Dissipation+Utilization=Self−Organization. https://www.mdpi.com/1099-4300/25/2/229
- https://harrison-69935.medium.com/the-arrow-of-functional-complexity-reimagining-physics-part-7-de359cddfb6a
- https://en.wikipedia.org/wiki/Principle_of_maximum_entropy
- https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence
