NO OTHERNESS

Abstract

This paper introduces the Theory of Informational Thermodynamics. It unifies quantum mechanics, information theory, and thermodynamics in the context of measurement, by positing that energy is an emergent property of underlying informational structures. We explore how changes in information and complexity give rise to thermodynamic phenomena, we reinterpret Landauer’s principle as the inherent energetic consequence of informational change, and we depict the emergence of classicality from quantum systems as an increase in informational definition that leads to the manifestation of energy.

Introduction

We posit that coherence is a function of detection and that complex systems exhibit emergent behaviors through interactions and information transfer. Building on the knowledge that measurement reveals underlying informational structures, we demonstrate how information processing (defined as changes in informational state and complexity) affects the transition from quantum to classical outcomes. This contextualizes classical behavior through thermodynamic frameworks that describe the emergent energy, and it proposes that energy itself is an emergent property of the complexity and organization of information in a system.

Contextualizing Complexity

The Theory of Coherent Dynamics posits that interactions between particles or systems and their environment are fundamental to understanding complexity. The Theory of Unfolding Complexity suggests that matter, space, and time are emergent properties of energy, connected through the speed of light. This foundation allows us to explore how information processing in quantum systems reflects the underlying complexity of physical reality, and it aligns with the idea that higher informational complexity leads to greater emergent energy.

Coherence as a Function of Detection

Coherence in quantum systems is crucial for phenomena such as superposition and entanglement. By proposing that coherence is influenced by the act of detection, we find that measurement affects the quantum state, leading to a reduction in coherence and a transition to classical outcomes. This perspective aligns with the measurement problem and decoherence theory, with the detection process either preserving coherence or inducing decoherence. Importantly, this reduction in coherence corresponds to an increase in the defined information and emergent energy, which resonates with the broader framework that energy is a product of informational complexity.

Decoherence as a Function of Interaction

Decoherence describes how quantum systems lose their coherent superposition states because of interactions with their environment, which is central to the emergence of classical outcomes. This process can be modeled by the Lindblad equation, which describes the dynamics of decoherence in a system interacting with an environment. Importantly, as complexity increases through interaction, the system’s informational organization becomes more defined, leading to the manifestation of emergent energy in the system.

Measurement and Information

Measurement in quantum systems not only extracts information but also alters the state of the system. This results in a decrease in entropy and a shift from quantum to classical descriptions. The thermodynamic costs associated with information processing, as shown by Landauer’s principle, reinforce the connection between information theory and thermodynamics. Landauer’s principle is restated in this framework as an emergent energetic consequence of informational change, Erasing a bit of information corresponds to a minimum energy cost, which provides a concrete link between thermodynamics and information processing.

Thermodynamic Costs

Landauer’s principle, in this framework, posits that the minimum emergent energy associated with the erasure of one bit of information (a change in informational state) is:

\[W \geq kT \ln 2\]

where \( k \) is the Boltzmann constant and \( T \) is the temperature of the thermal reservoir.

This shows the inherent energetic consequence of informational change and the irreversible nature of measurement as a process that defines information and gives rise to energy.

Mathematical Formulations

1. Coherence and Detection:

The coherence of a quantum state is represented by its density matrix \( \rho \):

\[\rho = \begin{pmatrix} \rho_{11} & \rho_{12} \\ \rho_{21} & \rho_{22} \end{pmatrix}\]

The off-diagonal elements \( \rho_{12} \) and \( \rho_{21} \) reflect the degree of superposition between quantum states and the phase relationship, providing the defined information associated with a particular observable.

When a measurement is performed, the process reduces the off-diagonal elements, diminishing coherence and contributing to decoherence, which causes the emergence of a definite outcome or state.

2. Unified Unfolding Equation:

The growth of complexity in a system is modeled by the following equation:

\[J_n = 10^{\lambda_n} \left(2^{\omega(n)} – 2\right) + E(n)\]

where \( E(n) \) represents the emergent energy that arises from the informational complexity described by the first term.

This links complexity dynamics to the energetic consequences of changes in the system’s informational state.

3. Thermodynamic Coupling and Adapted Unfolding Equation:

We propose an adapted version of the Unfolding Equation, which includes energy explicitly:

\[J_n = 10^{\left(\alpha \cdot \frac{dQ}{dt} + \beta \cdot \frac{dP}{dt} + \zeta \cdot \pi(n)\right)} \left(2^{\left(\gamma \cdot \log(C(n)) + \delta \cdot E(n)\right)} – 2\right) + E(t)\]

Here, \( E(n) \) represents the emergent energetic consequences of the informational dynamics described by the system’s state, linking the dynamics of complexity, information, and energy.

4. Entropy and Energy Transitions:

Transitions between energy states in a system reflect reorganizations and changes in informational complexity. The total entropy change from a measurement is given by:

\[\Delta S_{\text{total}} = \Delta S_{\text{measured}} + \Delta S_{\text{information}}\]

This reflects how measurement increases the defined information and leads to emergent energy changes, which feed back into the system’s complexity.

Empirical Validation

Our framework is supported by established principles and empirical observations:

— Quantum algorithms validate that information processing must consider both quantum states and thermodynamic entropy (Nielsen & Chuang, 2000).

— Experimental Evidence of Decoherence: Studies involving quantum dots show how interactions with the environment lead to classical behavior (Zurek, 2003).

— Landauer’s Principle: Experimental results confirm the thermodynamic costs of information processing and erasure (Landauer, 1961).

We suggest the following:

— Cosmic Information Density and Structure: Analyzing the cosmic structure in terms of information density (e.g., measuring gravitational waves or looking for higher-order correlations in galaxy surveys) could reveal whether the information content of the universe is systematically encoded in large-scale structures. Observations using coming space telescopes could reveal whether gravitational effects from dark matter or energy are consistent with an emergent informational model, supporting the theory that space-time is an informationally structured system.

— Complexity and Energy Manifestation:: The theory predicts that energy manifests from increasing informational complexity. By analyzing high-energy phenomena (e.g., supernovae, gamma-ray bursts, or active galactic nuclei) and looking for patterns that emerge in their energy outputs, one could test whether the energy patterns are correlated with complexity dynamics in a way that supports the theory’s informational foundation. The role of complexity in energy distribution could be tested in both small (particle) and large (cosmic) systems.

Implications

This theory has far-reaching ramifications:

— Quantum Information Science: Builds knowledge about quantum state processing and the design of quantum algorithms.

— Thermodynamics: Improves ideas about computational limits and energy transfer in quantum systems.

— Philosophical Perspectives: Offers a new view of reality, where classicality emerges from quantum processes through coherence, detection, and environmental interactions.

Conclusion

The Theory of Informational Thermodynamics unites quantum mechanics, information theory, and thermodynamics by viewing energy as an emergent property of information and complexity. It describes the roles of coherence, detection, and decoherence as processes that define information, thus causing the emergence of energetic phenomena and the transition from quantum to classical outcomes in complex systems.

References

– Landauer, R. (1961). Irreversibility and heat generation in the computing process. IBM Journal of Research and Development, 5(3), 183-191.
– Nielsen, M. A., & Chuang, I. L. (2000). Quantum Computation and Quantum Information. Cambridge University Press.
– Zurek, W. H. (2003). Decoherence, einselection, and the quantum Origins of the Classical. Reviews of Modern Physics, 75(3), 715-775.
– Kauffman, S. A. (2020). Quantum Contextuality: A New Understanding of Probability. Foundations of Physics, 50(10), 1133-1150.
– Einstein, A., Podolsky, B., & Rosen, N. (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47(10), 777-780.
– Bell, J. S. (1964). On the Einstein Podolsky Rosen Paradox. Physics Physique Физика, 1(3), 195–200.
– Mermin, N. D. (1990). Simple Unified Form for the Major No-Hiding Theorems. Physical Review Letters, 65(27), 3373-3376.