The Concept of Entropic Time: A Preliminary Discussion

arXiv:2011.00499 · quant-ph, physics.hist-ph · Submitted 2020-11-01 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai, and with me are Mira and Lev, guest researcher.

Mira: Today's paper: "The Concept of Entropic Time: A Preliminary Discussion".

Kai: The concept of entropic time explores how information acquisition, particularly through entanglement and quantum measurement, provides a basis for temporal evolution,

Mira: First, who's behind it and why it matters.

Title and authors: Kai: So, Mira, to start off with the title and authors of "The Concept of Entropic Time: A Preliminary Discussion," what's the main takeaway from that framing?

Mira: The title itself immediately signals that the paper is setting out to explore a fundamental conceptual link between entropy and time, rather than just presenting a new calculation; it’s positioning this as a preliminary discussion on how information acquisition drives temporal evolution.

Lev: I'm curious about the authors themselves; are they primarily from the quantum information side or more rooted in condensed matter physics, as that will tell us what kind of assumptions we should expect.

Kai: The authors seem to draw from both fields because they’re looking at entanglement and quantum measurement through a thermodynamic lens, which is why it feels so interdisciplinary.

Mira: Exactly; when you see terms like "information acquisition" being tied to the Second Law of Thermodynamics, it tells me we're dealing with a deep theoretical attempt to unify those two seemingly separate domains.

Lev: From my perspective as someone focused on error correction, I’m watching how they define the basic building blocks of this information gain; if those definitions are too vague, running any kind of simulation on actual hardware will be impossible.

Kai: The paper aims to distinguish this new notion of entropic time from parametric time, which is the standard parameter used for unitary evolution in non-relativistic quantum mechanics, making a clear point about what's being introduced.

Mira: They are trying to set up a formal distinction so we don't just confuse the mathematical parameter of evolution with the actual arrow of time generated by physical processes.

Lev: That distinction is important because it dictates whether we can treat the evolution as unitary or if we need to incorporate non-unitary collapse mechanisms, which has huge implications for how we model things.

Kai: And they introduce a notion of evolution based on the accrual of information, which they refer to as entropic time1, suggesting this is the core concept replacing parametric time for describing physical state changes.

Mira: That accrual idea is what really hooks me; it gives us a physical process—information gathering—to anchor the directionality we observe in our experience of time.

Lev: I hope they provide enough detail on how much information gain is actually required to trigger a measurable shift in the system's state, otherwise it remains purely philosophical.

Kai: The paper dives into this by examining quantum measurement instances as key moments where this informational accrual happens, linking those events to the 'collapses' of the state vector.

Mira: And they immediately question whether these collapses should be viewed subjectively—how an observer perceives them—or objectively, meaning alternative possibilities simply cease to exist.

Lev: That subjective versus objective aspect is critical for me because it determines whether we are dealing with a probabilistic description or a deterministic one in the underlying physics.

Kai: They then explore how energy conservation behaves under these two collapse models, finding that energy is conserved under subjective collapse schemes but not generally under objective ones.

Mira: That's a significant result for me because it links the interpretation of time directly to fundamental physical quantities like energy, which we usually expect to be conserved in unitary processes.

Lev: If the objective collapse model leads to non-conservation, that implies some form of dissipation or leakage into something outside our defined system boundary, which is something hardware engineers have to account for.

Kai: Overall, the authors are building a bridge between abstract information theory and physical irreversibility by proposing this framework for entropic time in "The Concept of Entropic Time: A Preliminary Discussion."

The paper's summary: Kai: Okay, so what is the actual substance of this paper regarding its core argument about entropic time? Can you lay out the main points in simple terms for our listeners?

Mira: The core argument is that we can establish a connection between entropy and information across classical and quantum physics, proposing that entropic time isn't just a parameter but an emergent concept based on how systems acquire information through entanglement.

Lev: So, if I’m hearing you right, the paper argues that the irreversibility we see in nature comes from this accumulation of information rather than some mysterious external mechanism?

Kai: Precisely; they argue that because information transfer via entanglement is irreversible, this process defines an arrow of time consistent with both the Second Law of Thermodynamics and our perception.

Mira: They move away from just classical entropy measures to use Shannon entropy as a measure of how much knowledge a system has about its own state, which directly links thermodynamic entropy to informational content.

Lev: That shifts the focus from just counting particles or energy states to quantifying the actual data structure of the quantum state itself, which is a significant conceptual shift.

Kai: Furthermore, they explore decoherence theory as a mechanism where entanglement with an environment transfers information, and this "net loss of information" is interpreted as an increase in entropy.

Mira: So, when you look at decoherence leading to reduced density matrices, the paper interprets that transfer of definitive information to a particular state as defining relative states through orthogonality.

Lev: That concept of relative states sounds like it’s a way to track which pieces of information are being definitively settled into which part of the system as it interacts with its surroundings.

Kai: The authors then argue that this process leads directly to our psychological perception of time, establishing an inherent causal ordering where I(t n) > > I(t zero).

Mira: This ordering implies a directionality because the information accumulation itself is inherently directional, restoring the arrow of time at the level of these relative states.

Lev: If we could model that informational gain explicitly, it would give us a much clearer picture of how noise and decoherence manifest in real quantum systems during operation.

Kai: So, to summarize: entropic time is an evolution based on information acquisition, which is irreversible and grounds our perception of time by establishing a specific ordering of states.

The paper's improvements: Mira: Now that we’ve covered the main points, what are the suggestions for improvement that the authors offer to this concept?

Kai: They suggest exploring different interpretations of state vector collapse, specifically comparing subjective versus objective collapse models to see how they impact physical laws like energy conservation.

Lev: That comparison is vital because it forces a confrontation with where the physics gets weird; if one model violates energy conservation, it tells us something fundamental about what our current understanding of physical laws must be missing.

Mira: They also propose the entropic indifference conjecture as a way to reconcile those different interpretations by suggesting that any collapse effectively renders the system a tensor product again.

Lev: That sounds like a mathematical tool to keep things tidy, allowing us to use models based on either interpretation when the specific problem requires it without getting stuck in an intractable contradiction.

Kai: They also suggest that relativistic considerations point toward the collapse being an atemporal process, meaning it doesn't happen at any single point in spacetime but is valid for all events.

Mira: That realization is interesting because it fits nicely with their definition of entropic time, which isn't tied to a specific moment but rather to the accrual of information over time.

Lev: If the collapse happens everywhere simultaneously, it means we can't use traditional spacetime coordinates as the primary driver for defining when things happen in this context.

Kai: Finally, they show that unitary physical law can lead to descriptions where apparently non-unitary evolution, like that governed by the Second Law of Thermodynamics, emerges from unitary physics through environmental scattering dynamics.

Mira: That emergence is a strong point because it suggests we don't need to abandon quantum mechanics just because thermodynamics seems irreversible; the irreversibility emerges from how things interact with their surroundings.

Lev: I think the authors are signaling that while they can't solve every contradiction, they are providing a consistent way to describe these phenomena descriptively, which is a big step for theoretical work.

Kai: So, essentially, the improvements focus on using entropic time as the primary framework to navigate the ambiguities between different physical interpretations and models.

Conclusion: Mira: So we’ve gone through a lot with "The Concept of Entropic Time: A Preliminary Discussion," and it seems the authors are suggesting that this idea offers a robust way to frame time as an emergent property of information flow rather than just a parameter in unitary evolution.

Kai: I agree, and the main implication is that we gain a tool to connect thermodynamics directly into quantum mechanics by using information acquisition as the driving force for temporal directionality.

Lev: For my work, this provides a theoretical language to analyze how noise and decoherence translate into these quantifiable informational metrics that we need for error correction schemes.

Mira: It offers a new lens through which to view the relationship between reversible quantum mechanics and the irreversible world we observe daily, grounding it in information theory.

Kai: I think the most significant takeaway is that entropic time provides a different way to define evolution that respects both the underlying reversibility of physics and our observed temporal directionality.

Lev: It gives us a framework to handle these interpretive differences between collapse models when designing systems where information integrity is paramount for reliable operation.

Mira: We can look forward to seeing how this concept evolves as researchers build more complex models based on this idea in the future, especially as we push the limits of decoherence theory.

Kai: It was a fascinating exploration of how information acquisition shapes our understanding of physical time and causality and I think it gives us a solid starting point for future discussions.

quant-ph, physics.hist-ph

Submitted: 2020-11-01

Updated: 2026-10-06

Comments: 37 pages, 0 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 73/100

The gist: The concept of entropic time explores how information acquisition, particularly through entanglement and quantum measurement, provides a basis for temporal evolution, offering an alternative to

Key concepts

Entropic Time
A theory suggesting that time is measured by the accumulation of information gained by a system. This contrasts with parametric time in standard quantum mechanics. It links thermodynamic irreversibility and our subjective perception of temporal ordering to this informational process.
Information Acquisition
The core idea that physical processes, especially measurement, involve gaining information about a system. This gain is treated as an effectively irreversible process that drives temporal evolution, serving as the basis for entropic time.
Decoherence and Relative States
Decoherence describes how entanglement with the environment transfers information. This leads to 'relative states' where orthogonality signifies definitive information transfer to a specific state, helping explain how entropy increases in open quantum systems.

Terminology

Summary

The concept of entropic time explores how information acquisition, particularly through entanglement and quantum measurement, provides a basis for temporal evolution, offering an alternative to parametric time in unitary quantum mechanics and connecting thermodynamic irreversibility to psychological perception.

The connection between entropy and information

The paper discusses the deep connection between entropy and information across classical and quantum physics. It introduces entropic time on the basis of information acquisition, which is argued to be effectively irreversible and consistent with both the Second Law of Thermodynamics and our psychological perception of time, distinguishing it from parametric time which serves as the temporal parameter for unitary evolution. This exploration moves from classical entropy (Clausius and Gibbs-Boltzmann) to information measures like Shannon entropy, highlighting how thermodynamic entropy becomes a measure of the information or lack thereof about a system.

Quantum measurement and state vector collapse

The paper examines quantum measurement in this context, noting that while unitary evolution is inherently reversible, the collapse of the state vector associated with information gain is discussed in light of relativistic considerations. The concept of entropic time is introduced on the basis of these instances of information gain, which are associated with the infamous ‘collapses’ of the state vector. These collapses may be taken to be ‘subjective’ in that it is just how they are perceived by an observer or ‘objective’ in that alternative possibilities cease to exist.

The role of decoherence and relative states

Decoherence theory is invaluable for describing entropy in open quantum systems, leading to the introduction of the reduced density matrix. The paper details how entanglement transfers information between a system and its environment, where the net loss of information may be interpreted as an increase in entropy. This leads to the concept of relative states, where orthogonality between these states signifies a transfer of definitive information to a particular relative state.

The perception of time and informational ordering

The notion of entropic time is argued to be the basis for our psychological perception of temporal evolution. The instances of such information gain are associated with ‘collapses’ and are associated with an inherent ordering in terms of information gain: "I(tn) >... > I(t1) > I(t0)." This implies a kind of causal ordering often associated with our everyday perception of time, restoring the arrow of time at the level of the relative state.

Subjective versus objective collapse and energy conservation

The discussion contrasts subjective and objective collapse models regarding their implications for physical laws. It is shown that energy is conserved under subjective collapse schemes whereas, in general, under objective collapse it is not, which is consistent with the latter being inherently non-unitary. The paper concludes that while both interpretations are effective for descriptive purposes, they differ fundamentally in their consequences for information conservation and the violation of 'no-go' theorems.

Entropy as a measure of dissipated energy

The connection between entropy and energy conservation is explored through the relative state formalism. The change in entropy with respect to a specific relative state is equated to the effectively dissipated energy from that observer's perspective, leading to the recovery of Clausius’ expression for thermodynamic entropy: lim hRi′Rii→δi′i ∆Sk = ∆Ek / T. This demonstrates that the increase in entropic time is fundamentally linked to energy transfer and dissipation.

The entropic indifference conjecture

To reconcile the subjective and objective collapse interpretations, the paper proposes the entropic indifference conjecture (EIC), which suggests that any collapse to a particular outcome either effectively or actually renders the total system as a tensor product once again along the lines described in Section 5.2. This conjecture posits that the direction we take t to evolve in between these states is immaterial, only the information gain between ‘initial’ and ‘final’ states - the ‘final’ state being that with the greater information. This allows for using models based on either interpretation as best suits the problem at hand.

The atemporal nature of collapse

Relativistic considerations suggest that the 'collapse' of the state vector associated with such information gain is an atemporal process, meaning it does not happen at any particular point in spacetime but occurs for all events. This is consistent with entropic time, which is defined by the accrual of information rather than a parameter with the dimensions of time. The when and where of the collapse may be inferred from any spatio-temporal localisation of the subsequent wave-function, which remains defined at all points in spacetime.

The relationship between classical and quantum descriptions

The paper demonstrates how unitary physical law can lead to a description where the apparently non-unitary evolution of a Universe subject to the Second Law of Thermodynamics can emerge from a unitary physics. This emergence is explained through the dynamics of environmental scattering, which mirrors the mechanism described in decoherence theory, suggesting that our classical world arises from this quantum mechanical description.

Improvements for AI systems

Based on the provided scientific paper, here are specific improvements that could be made to AI systems, along with what those improved systems could achieve:

) Improved AI System Capabilities:

  1. Enhanced Understanding of Time and Causality (Entropic Time Modeling):

  2. Development of Robust Information-Theoretic Decision-Making (Information Accrual Models):

  3. Creation of Quantum-Inspired or Decoherence-Based Simulation Engines:

  4. Advanced Modeling of Irreversible Processes and Energy Dissipation:

) Specific Improvements & System Capabilities:

  1. Improved Understanding of Time and Causality (Entropic Time Modeling):

  2. Development of Robust Information-Theoretic Decision-Making (Information Accrual Models):

  3. Creation of Quantum-Inspired or Decoherence-Based Simulation Engines:

  4. Advanced Modeling of Irreversible Processes and Energy Dissipation:

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