Conceptual Note: The Arrow of Time as an Emergent Property of Informational Change

Author: Juan Ignacio Oroz

Affiliation: National University of La Plata, Argentina

Abstract

This conceptual note proposes that the arrow of time is not a fundamental feature inscribed in the ultimate laws of nature, but an emergent property associated with informational change and the loss of informational accessibility in physical systems. Starting from the tension between the reversibility of many microscopic equations and the irreversibility that characterizes everyday experience, the note argues that temporal asymmetry arises when part of a system's information becomes inaccessible due to processes such as coarse-graining, environmental interaction, or the dispersion of correlations.

Within this framework, events are understood as distinguishable transitions between physical states, and temporal direction as the effective ordering that emerges when informational entropy increases. Time is therefore not treated as an ontologically primitive parameter, but as a relational variable reconstructed from the informational structure of states.

Illustrative examples include cosmological evolution from low initial informational entropy and black holes as extreme limits of informational inaccessibility, as well as recent results in controlled quantum systems suggesting that irreversibility depends on informational accessibility. The proposal does not aim to replace existing theories, but to conceptually reframe the role of time as the trace left by the evolution and concealment of information in physical systems.

Introduction

Our daily life is tightly anchored to the arrow of time. Without it, there would be no order, no routine; we would not know when it is day and when it is night. A life without time, in that sense, ceases to be life. We take for granted the existence of the past, the present, and the future, and we assume that time flows inevitably in a single direction. But what if this were not the case?

Before proceeding, it is important to clarify the ontological scope of this question. This note does not call into question the empirical validity of time as an operational magnitude, nor its usefulness in current physical theories. What is being questioned is its fundamental status: whether time should be regarded as a primary ingredient of reality or as a property that emerges from more basic physical structures.

When the problem is examined from the standpoint of fundamental physics, this intuitive picture begins to lose its apparent simplicity. The microscopic laws governing the dynamics of particles and fields are, for the most part, temporally reversible. Moreover, in deeper formulations - such as certain approaches to quantum gravity - time does not even appear as an explicit variable. This tension between everyday experience and the fundamental structure of physical theories constitutes the starting point of the present note.

From this observation arises the central hypothesis: time, and in particular its arrow, is not a fundamental entity but an emergent property associated with informational change in physical systems.

Conceptual framework: information, entropy, and physical systems

In order to proceed, it is necessary to specify the concepts involved in the framework more precisely.

By physical system we mean any set of degrees of freedom that can be described in terms of well-defined physical states, whether using a classical or quantum framework. Every real system is, explicitly or implicitly, in interaction with an environment, which makes it an open system.

By information we mean the distinguishable content of a physical state, that is, whatever allows one state to be differentiated from another within a set of possibilities. In classical systems, this information can be quantified through Shannon entropy; in quantum systems, through the von Neumann entropy associated with a density matrix.

By physical state we mean a classical or quantum description of the relevant variables that characterize a system within a given effective framework. It does not necessarily represent the system's complete microscopic totality, but rather the physically significant information required to describe its evolution.

By open system we mean one that exchanges information, energy, or correlations with an environment. As discussed above, in practice, every real physical system is open, and its dynamics cannot be considered completely isolated from its surroundings.

By event we mean not a primary entity, but a distinguishable transition between physical states. Every event implies an informational difference and therefore an effective distinction within the system's state space.

By informational accessibility we mean the degree to which the information associated with a physical state can be recovered, controlled, or correlated by an observer or subsystem. The loss of accessibility - not the destruction of information - is the operational origin of irreversibility.

By coarse-graining we mean the procedure by which microscopic degrees of freedom that are irrelevant for an effective description are discarded, yielding an incomplete but operationally useful representation of the system.

By informational entropy we mean that entropy quantifies the loss of informational accessibility associated with an effective description of the system. It does not measure disorder in a qualitative sense, but rather the practical impossibility of distinguishing between physical states that were previously differentiable.

By arrow of time we mean the effective asymmetry between consecutive physical states associated with the irreversible loss of accessible information. It does not constitute a fundamental property of dynamical laws, but rather an emergent feature of the informational description.

Scales of temporal emergence

A crucial point is that the relevant information usually does not correspond to the system's complete microscopic state, but rather to an effective description, limited by the observer's access, by coarse-graining, or by entanglement with the environment. From this perspective, entropy does not measure "disorder" in a vague sense, but a loss of informational accessibility.

It is essential here to distinguish between two notions that are often conflated: the reversibility of dynamical equations and informational irreversibility. The proposal of this note rests on the idea that the arrow of time does not arise from a fundamental asymmetry in the laws themselves, but from an effective asymmetry in access to physical information.

From the succession of events to the arrow of time

What we commonly call time manifests operationally as an ordered succession of events. However, events are not primitive entities: each event corresponds to a difference between physical states. And every difference between states implies an informational distinction.

This observation suggests that if temporal order is grounded in a succession of differences, and differences are encoded as information, then the arrow of time must be closely linked to the behavior of information.

In particular, when a system evolves in such a way that part of its information becomes inaccessible - through dispersion, entanglement, or coarse-graining - an effective asymmetry emerges between earlier and later states. That asymmetry is what we experience as temporal direction.

From information to perceived time

Emergence without fundamental time

A key aspect of the proposal is that irreversibility can emerge even in the absence of a fundamental time. Consider a system described by reversible dynamical rules, yet observed through an incomplete informational description. If the dynamics are iterated and, at each step, irrelevant microscopic information is discarded, informational entropy increases.

Here, the "arrow" does not arise because time flows, but because accessible information decreases. The ordering of states can be reconstructed a posteriori according to their informational content, giving rise to an effective notion of past and future. Within this framework, time appears as an emergent variable rather than as a basic ontological parameter.

Implicitly, this perspective suggests the possibility of defining a magnitude associated with the system - a measure of accessible information - whose variation orders the states without introducing a prior time parameter. The flow between states can then be understood as a relational flow, defined by changes in informational structure.

Illustrative physical examples

To illustrate the idea clearly and concisely, consider the example of days on Earth. Hundreds of millions of years ago, Earth's rotation was considerably faster, and days were much shorter than the present 24 hours. Gravitational interaction with the Moon has transferred angular momentum from Earth's rotation to the lunar orbit, progressively slowing the planet's rotation. In the future, the length of the day will change again.

This fact shows that some of our familiar temporal units are not absolute, but dependent on the physical state of a particular system. The "day" is not a fixed entity, but a relational construction based on accessible information about the Earth-Moon dynamical system. In this sense, measured temporal units may emerge from physical relations, rather than from an unchanging background.

Take black holes, for another example. Black holes represent the extreme limit of the loss of accessible information. The Bekenstein-Hawking associates an entropy with the black hole horizon, often interpreted as a measure of the information inaccessible to an external observer. From this perspective, extreme gravitational processes introduce a temporal arrow associated with the practical impossibility of recovering that information. Irreversibility does not arise here from a violation of fundamental laws, but from an insurmountable informational barrier for the external observer.

The Big Bang and low initial entropy

The early universe is characterized by an initial condition of extremely low informational entropy. As the universe evolves, tiny initial fluctuations grow under gravity, leading to the formation of stars, galaxies, and large-scale structure. In this process, correlations disperse, inaccessible degrees of freedom increase, and the cosmological arrow of time emerges.

Within this framework, the Big Bang is not merely an event "in" time, but the limit from which the very notion of time acquires physical meaning, linked to the informational evolution of the cosmos.

Experimental support and recent results

Recent theoretical and experimental work in quantum systems has strengthened the idea that the arrow of time can be connected to information, correlations, and the way a system is observed. In 2025, Guff, Shastry, and Rocco studied open quantum systems and showed that opposing effective arrows of time can emerge in reduced descriptions without requiring a fundamental violation of time-reversal symmetry. Related work on entanglement and thermodynamic arrows has also shown that correlations between subsystems can affect the apparent direction of irreversible processes. These results may support the notion that irreversibility is not fundamental, but rather a consequence of the loss or inaccessibility of information in physical systems.

Implications and avenues for formalization

As stated before, the idea presented here does not aim to replace existing theories, but to conceptually reorder the role of time. From this perspective, time ceases to be a basic ingredient and comes to be understood as an emergent property tied to the informational structure of physical systems and their relation to the environment.

This conceptual framework opens possibilities for more formal developments. Among these are the formulation of a minimal relational flow equation, a potential formalization in the context of open quantum systems, computational models associated with the loss of informational accessibility, and possible links with early cosmology and gravity problems.

Closing

If this perspective is correct, then the fundamental question is not why time flows, but what makes certain information become inaccessible. Within this framework, the arrow of time would not be a law written into the fabric of the universe, nor a background stage on which events unfold. Instead, it would emerge as the trace left by physical transformations as accessible information is dispersed, hidden, or lost to an effective description. Time would not be imposed by fundamental laws; it would emerge as the trace left by information when it is lost - a flicker of the past that, as it dissipates, reveals a prelude to what might become the future!

References

• Shannon, C. E. (1948). A Mathematical Theory of Communication. The Bell System Technical Journal. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x

  
  

• Barbour, J. (2012). Shape Dynamics. An Introduction. Quantum Field Theory and Gravity: Conceptual and Mathematical Advances in the Search for a Unified Framework. Springer Basel. https://doi.org/10.1007/978-3-0348-0043-3_13

  
  

• Barbour, J., Koslowski, T., & Mercati, F. (2014). The Solution to the Problem of Time in Shape Dynamics. Classical and Quantum Gravity. https://doi.org/10.1088/0264-9381/31/15/155001

  
  

• Barbour, J., Koslowski, T., & Mercati, F. (2013). A Gravitational Origin of the Arrows of Time. https://doi.org/10.48550/arXiv.1310.5167

  
  

• Barbour, J., Koslowski, T., & Mercati, F. (2016). Janus Points and Arrows of Time. https://doi.org/10.48550/arXiv.1604.03956

  
  

• Ellis, G. F. R. (2013). The Arrow of Time and the Nature of Spacetime. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. https://doi.org/10.1016/j.shpsb.2013.06.002

  
  

• Romero, G. E. (2023). Commentary: Physical time within human time. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2023.1092351

  
  

• Romero, G. E. (2016). A Formal Ontological Theory Based on Timeless Events. Philosophia. https://doi.org/10.1007/s11406-016-9697-8

  
  

• Guff, T., Shastry, C. U., & Rocco, A. (2025). Emergence of opposing arrows of time in open quantum systems. Scientific Reports. https://doi.org/10.1038/s41598-025-87323-x

  
  

• Jennings, D., & Rudolph, T. (2010). Entanglement and the thermodynamic arrow of time. Physical Review E. https://doi.org/10.1103/PhysRevE.81.061130

  
  

• Buchholz, D., & Fredenhagen, K. (2023). Arrow of Time and Quantum Physics. Foundations of Physics. https://doi.org/10.1007/s10701-023-00728-4

  
  

• Barbour, J. (1999). The End of Time: The Next Revolution in Our Understanding of the Universe.

  
  

• Rovelli, C. (2017). The Order of Time.

  
  

• Von Neumann, J. (1932). Mathematical Foundations of Quantum Mechanics.