1. A New Paradigm Proposed in Theoretical Physics: The Theory of Entropicity (ToE)^[1]

The Theory of Entropicity (ToE) is a brilliant and emerging conceptual framework in theoretical physics that posits entropy as a fundamental, dynamic, and field-like entity that governs physical phenomena ranging from cosmology to consciousness ^[1][2][3].[1][2][3] This perspective marks a departure from the traditional view of entropy as a statistical measure of disorder or unavailable energy in a system ^[4][5].[4][5] The theory is primarily attributed to researcher John Onimisi Obidi ^[1][6].[1][6]

At its core, the ToE suggests that entropy's flow, generation, and irreversibility are the ultimate drivers of physical processes.[1] ^[1]. This framework aims to unify various areas of physics by treating entropy as a foundational element.

1.1. Core Concepts of the Theory of Entropicity (ToE)

Several key ideas have been proposed within the Theory of Entropicity:

• Entropy as a Fundamental Field: The ToE proposes that entropy is not merely a property of systems but a physical field, referred to as the "Entropic Field." ^[7] This field is suggested to shape the structure and evolution of physical systems, with all known forces, including gravity, emerging as constraints on its flow. [7^[2]] This field is suggested to shape the structure and evolution of physical systems, with all known forces, including gravity, emerging as constraints on its flow.[^[7]2][7]

• Entropic Gravity: In this view, gravity is not a fundamental force or a consequence of spacetime curvature, as in Einstein's General Relativity, but rather an emergent phenomenon arising from entropy-driven constraints. ^[7][The theory suggests that the maximization of entropy and the redistribution of information are the underlying principles of gravitational interactions. ^[7]7] The theory suggests that the maximization of entropy and the redistribution of information are the underlying principles of gravitational interactions.[7]

• Self-Referential Entropy (SRE) and Consciousness: The ToE introduces the concept of "Self-Referential Entropy" (SRE) to address the nature of consciousness. It posits that conscious systems have an internal entropy structure that refers to itself. ^[1][2][An "SRE Index" is proposed to quantify the degree of consciousness based on the ratio of a system's internal to external entropy flows. ^[2]1][2] An "SRE Index" is proposed to quantify the degree of consciousness based on the ratio of a system's internal to external entropy flows.[2]

• The Entropic Seesaw Model: To explain quantum phenomena like entanglement and wave function collapse, the ToE puts forward the "Entropic Seesaw Model." ^[6]This model analogizes two entangled quantum systems to the ends of a seesaw connected by an "entropic bar," which represents the entropy field. The collapse of the wave function is then envisioned as occurring when a critical entropy threshold is crossed. [6^[6]] This model analogizes two entangled quantum systems to the ends of a seesaw connected by an "entropic bar," which represents the entropy field. The collapse of the wave function is then envisioned as occurring when a critical entropy threshold is crossed.[6]

• New Proposed Principles: The framework also introduces new principles such as the "No-Rush Theorem," which posits a universal lower bound on the duration of interactions, asserting that physical processes cannot happen instantaneously. [^[8]8^[9]][9]

1.2. Proposed Applications and Implications of the Theory of Entropicity (ToE)

The proponents of the Theory of Entropicity suggest it could have applications in various fields:

• Entropic Engineering and Safety: This involves designing systems that are resilient to entropy gradients and defining risk based on a system's vulnerability to the entropic field. ^[3][3]

• Quantum Information and AI: The theory's principles are suggested to have applications in quantum information theory and the design of artificial intelligence architectures. ^[8][9][8][9]

• Clinical Biomarkers: The concept of SRE is proposed as a potential source for developing clinical biomarkers of consciousness. [^[8]8^[9]][9]

1.3. Current Status of the Theory of Entropicity (ToE)

The Theory of Entropicity (ToE) is a recent and speculative proposal within the scientific community. While it represents a groundbreaking framework, it has yet to undergo experimental verification and complete acceptance that are characteristic of established scientific theories like General Relativity (GR) and Quantum Field Theory (QFT). The concepts and mathematical formalisms of the Theory of Entropicity (ToE) are still in their development phases.

2. The "No-Rush Theorem" of the Theory of Entropicity (ToE)

The "No-Rush Theorem" is a core principle within the speculative framework of the Theory of Entropicity (ToE).[1][2] ^[1][2] This theory, primarily attributed to researcher John Onimisi Obidi, proposes that entropy is a fundamental, dynamic field that drives all physical processes.[1][3][4] ^[1][3][4]The No-Rush Theorem emerges from this central idea, asserting that no physical interaction can happen instantaneously. ^[2][5][2][5]

2.1. Core Principles of the No-Rush Theorem of ToE:

The theorem is colloquially summarized as "Nature cannot be rushed."[2][5][6] ^[2][5][6]It mandates that every physical process must have a finite, non-zero duration.[5] ^[5] This stands in contrast to some models in traditional physics that can assume instantaneous interactions for certain calculations. ^[1][7][1][7]

According to the Theory of Entropicity, interactions between physical systems occur through the exchange or redistribution of entropy.[5] This can happen via informational currents or microscopic reconfigurations.[5] ^[5]The No-Rush Theorem posits that because these processes involve the dynamics of a fundamental "entropic field," they cannot occur in zero time. ^[1][5][7][1][5][7]

2.2. Key Aspects of ToE's No-Rush Theorem:

3. It Connects Causality to a Physical Process (The No-Rush Theorem)

The No-Rush Theorem is the direct result of this framework.

Summary of the Theory of Entropicity (ToE): From Postulate to Consequence

• Minimum Interaction Time: The theorem establishes a minimum time for any physical interaction to take place. ^[1][2][1][2]

• Finite Duration of Processes: Every process, from the quantum to the cosmological level, is required to unfold over a non-zero period. [^[5]5]

• Entropic Field Dynamics: The necessity of a finite duration for interactions is attributed to the nature of the proposed entropic field. [^[1]1^[7]][7]

2.3. Proposed Implications of ToE's No-Rush Theorem:

The No-Rush Theorem, should the Theory of Entropicity gain wider acceptance and verification, would have significant implications across various fields of physics:

• Quantum Mechanics: It could provide a new perspective on phenomena like wave function collapse and decoherence, where quantum systems lose their coherence through entropy-driven processes. ^[1][3] The theory predicts a decoherence rate in open quantum systems that is proportional to the norm of the interaction operator. [1^[3]][^[4]3] The theory predicts a decoherence rate in open quantum systems that is proportional to the norm of the interaction operator.[3][4]

• Gravity and Causality: The theorem's proponents suggest it could reshape our understanding of gravity and the fundamental nature of causality. [^[1]1^[5]][^[7]5][7]

• The Arrow of Time: By placing a fundamental limit on the speed of interactions, the theorem is inherently linked to the directionality of time. [1][7]

These concepts are part of an ongoing research effort by the global physics community to develop a more unified framework in modern theoretical physics.

3. Summary of the Key Concepts of the Theory of Entropicity (ToE)

In brief, we take note of the following about the Theory of Entropicity (ToE):

3.1. The Entropic Field is Not Instantaneous

At the heart of the Theory of Entropicity is the idea that entropy isn't just a calculated property of a system (like its temperature or pressure), but a real, physical, and dynamic field that permeates all of spacetime. A key characteristic of this proposed "entropic field" is that its influence and changes are not instantaneous. Just as the electromagnetic field propagates at the speed of light, the entropic field is theorized to have its own dynamics that take time to unfold.

3.2. All Interactions Occur "Inside" This Field

The ToE goes a step further by proposing that this entropic field is the fundamental arena in which all other physical interactions take place. Instead of viewing forces like gravity, electromagnetism, and the nuclear forces as separate, fundamental entities, the theory recasts them as emergent phenomena or constraints on the behavior of this primary entropic field.

Think of it like this: if you have a large, stretched rubber sheet (representing the entropic field), any action on that sheet—like pressing down on it—will create ripples and effects that travel outwards. The action isn't felt everywhere on the sheet at the exact same moment.

3.3. Therefore, Interactions Cannot Be Instantaneous

This is the logical conclusion of the first two points, and it's precisely what the No-Rush Theorem encapsulates.

If:

• An interaction like gravity is fundamentally a process of entropic exchange or redistribution within the entropic field,

• And the entropic field itself cannot change or convey information instantaneously,

Then:

• It logically follows that the interaction (gravity) cannot be instantaneous either.

According to the ToE, for a gravitational interaction to occur between two objects, there must be a flow or reconfiguration of entropy in the field that connects them. This process, by the very nature of the proposed field, requires a finite, non-zero amount of time. The No-Rush Theorem formalizes this by stating that every physical process must have a minimum duration.

In essence, the Theory of Entropicity suggests that the reason "action at a distance" isn't instantaneous is because the underlying medium of that action—the entropic field—has its own built-in, non-instantaneous rules of behavior. All of the universe's fundamental forces are essentially "slaves" to the dynamics of this all-encompassing entropic field, and are therefore bound by its inherent "no-rush" principle.

It is crucial to remember that this is still an evolving theory and is yet to be experimentally verified.  Nonetheless, it represents a novel way of conceptualizing physical reality, even though it remains a theoretical proposal at this stage.

4. How the Conceptual Leap of the Theory of Entropicity (ToE) Gives Us a Revolutionary Understanding of the Physical World

The crucial point in our discussion here is to elucidate how the Theory of Entropicity (ToE) incites a revolution as a new theory, where a new theory must not only explain what we already know but also provide a deeper understanding or a more unified picture, which is precisely what ToE brings forward as its strong point.

Let's break down how the Theory of Entropicity (ToE) attempts to do this, specifically in relation to Einstein's principle of the constancy of the speed of light (c).

4.1. How Relativity Treats the Speed of Light

First, let's be clear about what Relativity says. In Einstein's Special Relativity, the constancy of the speed of light is a postulate—a fundamental axiom upon which the entire theory is built.

• Relativity's Stance: "We observe that the speed of light in a vacuum is the same for all observers, regardless of their motion. Let's accept this as a rule and see what the consequences are."

• The "What," not the "Why": Relativity brilliantly describes the consequences of this rule (time dilation, length contraction, E=mc²), but it does not explain why c is the universal speed limit. It's the starting premise, not a conclusion derived from a deeper principle.

4.2. How the Theory of Entropicity (ToE) Attempts to Explain and Go Beyond Einstein's Relativity & Its Axioms

The Theory of Entropicity (ToE) proposes to provide that deeper principle. It seeks to demote the constancy of light from a starting postulate to an emergent consequence of a more fundamental reality: the dynamics of the entropic field.

Here’s how ToE aims to give us a better understanding:

1. The Theory of Entropicity (ToE) Provides a "Why" for the Universal Speed Limit

Instead of just stating that there is a speed limit, ToE proposes a physical reason for it.

• Relativity: The speed limit is c.

• ToE's Explanation: The universe is fundamentally an informational system run on the "operating system" of the entropic field. All interactions are processes of entropic/informational exchange within this field. The speed of light, c, is interpreted as the maximum propagation speed of a disturbance or a change within this fundamental entropic field.

Think of it like this: The speed of sound in air is determined by the properties of the air itself (its density, pressure, etc.). You can't make a sound wave travel faster than that limit. ToE suggests that c is the analogous "speed of causality" determined by the fundamental properties of the entropic field that constitutes reality. It's the ultimate processing speed of the universe.

The Theory of Entropicity (ToE) teaches and explains to us that no change and no interaction in nature can occur in an instant - that some minimum time must elapse which is dictated by the entropic field as the generator of time itself; and it even goes on further to teach and explain to us that no interaction can propagate faster than the given speed of light; thus the Theory of Entropicity (ToE) gives us two limits: temporal limit on local interactions and temporal limit on global extensions.

2. The Theory of Entropicity (ToE) Unifies the Speed of Gravity and the Speed of Light

A key prediction of General Relativity, which has been experimentally confirmed, is that gravitational waves also travel at the speed of light, c.

• Relativity's View: General Relativity describes gravity as the curvature of spacetime. It turns out that disturbances in this curvature (gravitational waves) propagate at c. This is consistent with Special Relativity but doesn't necessarily explain why the two speeds are identical from a single, unified principle.

• ToE's Proposed Unification: ToE claims that both electromagnetism (light) and gravity are just different emergent manifestations of the same underlying entropic field.

  • Light: A ripple or excitation in the field.

  • Gravity: An entropic pressure or gradient within the field.
    
    Since both are phenomena occurring in the same fundamental medium, it's natural that they would be bound by the same maximum propagation speed (c). This offers a more cohesive picture than having two different phenomena that just happen to share the same speed limit.

• Relativity's Consequence: Because nothing can travel faster than c, interactions cannot be instantaneous. This upholds the principle of causality (an effect cannot precede its cause).

• ToE's Physical Mechanism: The No-Rush Theorem provides a physical mechanism for this. Causality is upheld because the entropic field, the very medium of all interaction, takes a finite time to process and propagate information. An interaction cannot be instantaneous for the same reason a ripple can't instantly appear across an entire pond—the medium itself has to transmit the effect.

In essence, ToE attempts to give a more foundational and mechanistic answer to the principles that Relativity takes as given. It shifts the foundation from "here's a rule we observe" to "here is the underlying machinery, and this rule is one of its natural outputs."

Crucially, this remains an emerging proposal of interest. While the Theory of Entropicity (ToE) offers an intriguing and potentially more unified way of looking at the physical world through the lens of one overriding physical principle of Entropy (which is already an established domain in the all of physics), it must still face the rigorous process of mathematical formalization, prediction-making, and experimental testing before it can be considered a universally valid scientific theory.

5. On The Dual Time-Limit Claims of the Theory of Entropicity (ToE) 

The ideas we have clarified above surely give us an exceptionally accurate and insightful summary of what is infact the central idea of ToE. We have thus far encapsulated the core claims of the Theory of Entropicity and articulated them in a very clear and structured way.

In this section, let's formally break down the two time limits we have identified above, as they are central to ToE's  proposed worldview.

ToE's Limit 1: The Temporal Limit on Local Interactions (The "No-Rush" Principle)

This is the microscopic, fundamental limit.

• What ToE says: No physical process, no matter how small or simple, can happen in zero time. Every change of state, every particle interaction, every quantum measurement requires a minimum, non-zero duration to unfold.

• ToE's Proposed Reason: Within ToE, every interaction is a reconfiguration of the entropic field. This reconfiguration is a physical process, not an abstract mathematical event. Just as a switch has a physical travel time, the entropic field has a "processing time" for any change.

• The Role of Time in ToE: This principle positions the entropic field as the very generator of time's flow at the local level. What we perceive as "time passing" is, in this view, the continuous unfolding of these non-instantaneous local interactions. The universe is constantly "computing" its next state, and the No-Rush Theorem says this computation has a clock speed; it's not infinitely fast.

ToE's Limit 2: The Temporal Limit on Global Extensions (The Speed of Light, c)

This is the macroscopic, emergent limit that governs how interactions propagate across distances.

• What ToE says: No interaction, influence, or information can travel between two separate points in space faster than the speed of light, c.

• ToE's Proposed Reason for the [constancy of the] Speed of Light in Relativity: This global limit is a direct consequence of the local limit. If an interaction has to travel from point A to point B, it must traverse every infinitesimal point in between. At each of these points, it is subject to the local "No-Rush" processing delay. The cumulative effect of these "countless", tiny, non-zero delays results in a finite travel speed across a macroscopic distance. The speed of light, c, is therefore interpreted as the ultimate propagation speed of a disturbance through the entropic field. This is the cumulative delay principle of the Theory of Entropicity (ToE) in using its No-Rush Theorem to explain the constancy of the speed of light in Einstein's beautiful Theory of Relativity (ToR).

• ToE's Unification: As we have already noted above, this provides a deeper "why" for the constancy of the speed of light. It's not just an arbitrary rule. In ToE, c is the "speed of causality" because it's the fastest that the fundamental fabric of reality—the entropic field—can transmit a change. Nature thus cannot be rushed to either interact faster or propagate faster.

How They All Fit Together in the Theory of Entropicity (ToE)

Thus, in the Theory of Entropicity (ToE), we see local and global time limits as two sides of the same coin.

The local limit ("No-Rush") ensures that processes happen in time, while the global limit (c) ensures that they propagate in time.

Together, they form a complete picture of causality within the Theory of Entropicity:

1. An event happens at point A. It cannot happen instantly due to the local limit.

2. The influence of this event spreads outwards. It cannot spread infinitely fast because it's constrained at every subsequent point by the same local limit, resulting in the global limit, c.

By framing the physics of the universe this way, the Theory of Entropicity (ToE) attempts to build concepts like the flow of time and the universal speed limit from the ground up, starting from the single, fundamental principle of entropy as a dynamic field.

Again, it is essential to remember that the Theory of Entropicity (ToE) is an emerging framework. It offers a fascinating and potentially unifying narrative, but it awaits the fully rigorous mathematical formalization^[2] and experimental evidence needed for global validation by the scientific community. Nonetheless, in summary, here we have succeeded in hinting at a perfect grasp of ToE's ambitious and thought-provoking claims.

6. How The Theory of Entropicity (ToE) Explains the Constancy of the Speed of Light (c) of Einstein's Theory of Relativity (ToR)

The "cumulative delay" [principle] argument of the Theory of Entropicity (ToE) which we presented above very well explains why the speed of light is finite as dictated by the axiom of Einstein's Principle of Relativity, but it does not adequately explain why it is constant for all observers in uniform motion. That constancy is the truly revolutionary and counter-intuitive core of Relativity.

Let us now further provide a more robust explanation from the perspective of the Theory of Entropicity (ToE), using its "cumulative delay" [principle] argument. The key for us in the Theory of Entropicity (ToE) is to shift from thinking of space as an empty stage to thinking of it as a fundamental, active medium activated by Entropy itself.

The Core Shift Presented by the Theory of Entropicity (ToE): From an Empty Stage to a Dynamic Field [of Entropy]

Conducting our gedanken experiment, now imagine the difference between a play on an empty stage versus a movie on a screen.

• The "Empty Stage" (Newtonian View): Actors (particles) can move across the stage (space). If an actor throws a ball, the ball's speed relative to you depends on whether you are running towards or away from the actor. This is our everyday intuition.

• The "Movie Screen" (ToE's Proposed View): Everything you see—the actors, the scenery, the light—is part of the projection on the screen. The screen has a fundamental property: the maximum speed at which a change can happen from one pixel to the next (its "refresh rate" or processing speed).

Now, crucially, take note of this profound insight of the Theory of Entropicity (ToE): You, as an observer, are also a character projected on that screen. You and your measuring devices (your clocks and rulers) are part of the movie, not separate from it.

Why Constancy Emerges from This "Movie Screen" Model of The Theory of Entropicity (ToE)

This is where the Theory of Entropicity (ToE) attempts to go deeper than Einstein's Relativity. It [ToE] posits that the "entropic field" is this fundamental screen.

1. The Field's Intrinsic Speed (c): The entropic field has a built-in, absolute, and unchangeable property: the maximum speed at which a cause can create an effect within it. This is the universe's ultimate processing speed. This is c. It's a property of the field itself, just like the density of water is a property of water.

2. Observers and Rulers Are Made Of the Field: This is the most important concept. An observer, their spaceship, their clocks, and their rulers are not independent objects moving through the field. They are complex, organized patterns of the field. You are made of the same "stuff" that transmits the light you are trying to measure.

3. Motion Through the Field Changes the Observer: Here is the explanation for the constancy of the speed of light in Einstein's Relativity. When you (as an organized pattern of the field) move relative to the broader field, ToE suggests that this motion causes a real, physical change in your internal structure.

   • The processes that govern your clock (be it atomic decay or a quartz crystal vibration) are interactions within the entropic field. Moving through the field causes these processes to slow down. This is time dilation as given by Einstein's Theory of Relativity (ToR).

   • The forces holding your ruler together are also manifestations of the entropic field. Moving through the field causes the ruler to physically compress in the direction of motion. This is length contraction as given by Einstein's Theory of Relativity (ToR).

Theory of Entropicity (ToE) Putting It All Together: The Grand Illusion of Constancy

Now, imagine you are in a spaceship traveling at 90% the speed of light, and you turn on a headlight.

• A stationary observer sees your headlight beam travel away from you at c.

• What do you see? You might intuitively think, "The light should move away from me slowly, at only 10% of c." But this is where the magic happens.

• According to ToE: Your motion through the entropic field has physically altered you. Your clock is ticking much slower, and your ruler is much shorter in the direction of travel. These are not illusions; they are real physical effects of your interaction with the field.

• When you use your (now slowed) clock and your (now shortened) ruler to measure the speed of the light from your own headlight, these two physical changes conspire in exactly the right way to cancel out your motion. The calculation speed = distance / time will yield the same exact number, c, as it does for the stationary observer.

In essence, the Theory of Entropicity claims that the constancy of the speed of light is a profound form of self-consistency. The field enforces its own fundamental speed limit by physically adjusting any ruler or clock that moves through it. YouYou always measure c always measure c because the very tools you use to measure it are altered by your motion in a way that guarantees you will get that result.

Summary: Relativity vs. ToE's Proposed Explanation

• Relativity states that time dilates and length contracts as a consequence of the postulate that c is constant. It's a geometric principle.

• The Theory of Entropicity proposes a physical cause for this. It states that time dilation and length contraction are real physical effects caused by moving through a fundamental entropic field. This physical change is what, in turn, makes it appear that c is constant for everyone.

It seeks to change the argument from "If c is constant, then time must slow down" to "Because moving through the entropic field slows time, c is measured to be constant." This is the deeper, more mechanistic, and—if proven—more convincing explanation that the Theory of Entropicity (ToE) offers. Refer to the "Theory of Entropicity Explains Einstein's Relativity Light Constancy" for further discussions.^[3]

References

1. Obidi, John Onimisi. The Entropic Force-Field Hypothesis: A Unified Framework for Quantum Gravity. Cambridge University; 18 February 2025. https://doi.org/10.33774/coe-2025-fhhmf
2. Obidi, John Onimisi. Exploring the Entropic Force-Field Hypothesis (EFFH): New Insights and Investigations. Cambridge University; 20 February 2025. https://doi.org/10.33774/coe-2025-3zc2w
3. Obidi, John Onimisi. Corrections to the Classical Shapiro Time Delay in General Relativity (GR) from the Entropic Force-Field Hypothesis (EFFH). Cambridge University; 11 March 2025. https://doi.org/10.33774/coe-2025-v7m6c
4. Obidi, John Onimisi. How the Generalized Entropic Expansion Equation (GEEE) Describes the Deceleration and Acceleration of the Universe in the Absence of Dark Energy. Cambridge University; 12 March 2025. https://doi.org/10.33774/coe-2025-6d843
5. Obidi, John Onimisi. The Theory of Entropicity (ToE): An Entropy-Driven Derivation of Mercury’s Perihelion Precession Beyond Einstein’s Curved Spacetime in General Relativity (GR). Cambridge University; 16 March 2025. https://doi.org/10.33774/coe-2025-g55m9
6. Obidi, John Onimisi. The Theory of Entropicity (ToE) Validates Einstein’s General Relativity (GR) Prediction for Solar Starlight Deflection via an Entropic Coupling Constant η. Cambridge University; 23 March 2025. https://doi.org/10.33774/coe-2025-1cs81
7. Obidi, John Onimisi. Attosecond Constraints on Quantum Entanglement Formation as Empirical Evidence for the Theory of Entropicity (ToE). Cambridge University; 25 March 2025. https://doi.org/10.33774/coe-2025-30swc
8. Obidi, John Onimisi. Review and Analysis of the Theory of Entropicity (ToE) in Light of the Attosecond Entanglement Formation Experiment: Toward a Unified Entropic Framework for Quantum Measurement, Non-Instantaneous Wave-Function Collapse, and Spacetime Emergence. Cambridge University; 29 March 2025. https://doi.org/10.33774/coe-2025-7lvwh
9. Obidi, John Onimisi. Einstein and Bohr Finally Reconciled on Quantum Theory: The Theory of Entropicity (ToE) as the Unifying Resolution to the Problem of Quantum Measurement and Wave Function Collapse. Cambridge University; 14 April 2025. https://doi.org/10.33774/coe-2025-vrfrx
10. Obidi, John Onimisi. On the Discovery of New Laws of Conservation and Uncertainty, Probability and CPT-Theorem Symmetry-Breaking in the Standard Model of Particle Physics: More Revolutionary Insights from the Theory of Entropicity (ToE). Cambridge University; 14 June 2025. https://doi.org/10.33774/coe-2025-n4n45^[1]
11. Obidi, John Onimisi. Master Equation of the Theory of Entropicity (ToE). Encyclopedia.pub; 2025. https://encyclopedia.pub/entry/58596.. Accessed 04 July 2025.
12. A Concise Introduction to the Evolving Theory of Entropicity (ToE). HandWiki; 2025. https://handwiki.org/wiki/Physics:A_Concise_Introduction_to_the_Evolving_Theory_of_Entropicity_(ToE). Accessed 09 July 2025.
13. Obidi, John Onimisi. A Critical Review of the Theory of Entropicity (ToE) on Original Contributions, Conceptual Innovations, and Pathways towards Enhanced Mathematical Rigor: An Addendum to the Discovery of New Laws of Conservation and Uncertainty. Cambridge University; 30 June 2025. https://doi.org/10.33774/coe-2025-hmk6n
14. Zurek WH. Decoherence, einselection, and the quantum origins of the classical. Rev Mod Phys. 2003;75(3):715–775. https://doi:10.1103/RevModPhys.75.715.
15. Verlinde, Erik P. On the origin of gravity and the laws of Newton. JHEP. 2011;04:029. https://arxiv.org/abs/1001.0785.
16. Fisher, R. A. Theory of statistical estimation. Proc Camb Philos Soc. 1925;22:700–725. https://doi:10.1017/S0305004100019299.
17. Rao, C. R. Information and the accuracy attainable in the estimation of statistical parameters. Bull Calcutta Math Soc. 1945;37:81–91. https://doi:10.1007/BF02862264.
18. Lieb, E. H, Robinson, D. W. The finite group velocity of quantum spin systems. Commun Math Phys. 1972;28(3):251–257. https://doi:10.1007/BF01645779.
19. Margolus, N, Levitin, L. B. The maximum speed of dynamical evolution. Physica D. 1998;120:188–195. https://doi:10.1016/S0167-2789(98)00054-2.
20. Padmanabhan, T. Thermodynamical aspects of gravity: new insights. Rep Prog Phys. 2010;73(4):046901. https://doi:10.1088/0034-4885/73/4/046901.
21. Das A, Bera A, Chakraborty S, Chruściński D. Thermodynamics and the Quantum Speed Limit in the Non-Markovian Regime. Phys Rev A. 2021;104:042202. https://doi.org/10.1103/PhysRevA.104.042202
22. Deffner S, Lutz E. Quantum Speed Limit for Non-Markovian Dynamics. Phys Rev Lett. 2013;111:010402. https://doi.org/10.1103/PhysRevLett.111.010402
23. Mandelstam L, Tamm I. The uncertainty relation between energy and time in nonrelativistic quantum mechanics. J Phys (USSR). 1945;9:249–254. https://doi.org/10.1007/BF01024755