Entropy and Cosmological Arrows of Time

The usual proof of the CPT theorem does not apply to theories which include the gravitational field. Nevertheless, it is shown that CPT invariance still holds in these cases provided that, as has recently been proposed, the quantum state of the Universe is defined by a path integral over metrics that are compact without boundary. The observed asymmetry or arrow of time defined by the direction of time in which entropy increases is shown to be related to the cosmological arrow of time defined by the direction of time in which the Universe is expanding. It arises because in the proposed quantum state the Universe would have been smooth and homogeneous when it was small but irregular and inhomogeneous when it was large. The thermodynamic arrow would reverse during a contracting phase of the Universe or inside black holes. Possible observational tests of this prediction are discussed.

Zenodo, 2025

We investigate the fundamental nature of \emph{time‑reversal symmetry} and its progressive breakdown in complex, structured dynamical systems. Drawing on the fluctuation theorem and recent quantum time‑reversal experiments, we show that although microscopic laws remain reversible, the emergence of \emph{computational naturalness}, characterized by a compact \emph{calculation cone} for forward prediction and an expansive \emph{retrodiction sphere} for reversal, inevitably yields intrinsic irreversibility. We formalize this via the \emph{naturalness ratio}, comparing the informational requirements of reversal versus prediction, and demonstrate how structural complexity and causal constraints sharply curtail the duration of reversible dynamics. Concurrently, we introduce a formal measure of \emph{entropy relativity}: an \emph{observer‑relative entropy} based on a Kullback–Leibler divergence that reproduces Gibbs entropy in equilibrium while capturing nonlocal correlations. Applied to cosmology, entropy relativity reveals that the early Universe, maximally entropic in its co‑moving frame, appears low in entropy when measured against its later expanded state, resolving the low‑entropy initial condition puzzle. We classify systems into \emph{fully reversible}, \emph{entropy‑resistant}, and \emph{structurally irreversible} regimes, and examine the role of \emph{CPT symmetry} in preserving fundamental laws despite quantum‑level asymmetries. Together, these insights bridge microscopic reversibility and macroscopic irreversibility, offering a \emph{unified framework} for entropy relativity, computational naturalness, and the cosmological arrow of time.

Cosmic Update, 2011

The only widely accepted explanation for the various arrows of time that everywhere and at all epochs point in the same direction is the 'past hypothesis': the Universe had a very special low-entropy initial state. We present the first evidence for an alternative conjecture: the arrows exist in all solutions of the gravitational law that governs the Universe and arise because the space of its true degrees of freedom (shape space) is asymmetric. We prove our conjecture for arrows of complexity and information in the Newtonian N-body problem. Except for a set of measure zero, all of its solutions for non-negative energy divide at a uniquely defined point into two halves. In each a well-defined measure of complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows. Recognition of the division is a key novelty of our approach. Each solution can be viewed as having a single past and two distinct futures emerging from it. Any internal observer must be in one half of the solution and will only be aware of one past and one future. The 'paradox' of a time-symmetric law that leads to observationally irreversible behaviour is fully resolved. General Relativity shares enough architectonic structure with the N-body problem for us to prove the existence of analogous complexity arrows in the vacuum Bianchi IX model. In the absence of non-trivial solutions with matter we cannot prove that arrows of dynamical information will arise in GR, though they have in our Universe. Finally, we indicate how the other arrows of time could arise.

Entropy, 2021

The paper tries to demonstrate that the process of the increase of entropy does not explain the asymmetry of time itself because it is unable to account for its fundamental asymmetries, that is, the asymmetry of traces (we have traces of the past and no traces of the future), the asymmetry of causation (we have an impact on future events with no possibility of having an impact on the past), and the asymmetry between the fixed past and the open future, To this end, the approaches of Boltzmann, Reichenbach (and his followers), and Albert are analysed. It is argued that we should look for alternative approaches instead of this, namely we should consider a temporally asymmetrical physical theory or seek a source of the asymmetry of time in metaphysics. This second approach may even turn out to be complementary if only we accept that metaphysics can complement scientific research programmes.

Foundations of Physics, 2008

In several previous papers we have argued for a global and non-entropic approach to the problem of the arrow of time, according to which the "arrow" is only a metaphorical way of expressing the geometrical time-asymmetry of the universe. We have also shown that, under definite conditions, this global time-asymmetry can be transferred to local contexts as an energy flow that points to the same temporal direction all over the spacetime. The aim of this paper is to complete the global and non-entropic program by showing that our approach is able to account for irreversible local phenomena, which have been traditionally considered as the physical origin of the arrow of time. *

arXiv: General Relativity and Quantum Cosmology, 2006

Motivated by the mounting evidence for dark energy, here we explore the consequences of a fundamental cosmological constant $\Lambda$ for our universe. We show that when the gravitational entropy of a pure DeSitter state ultimately wins over matter, then the thermodynamic arrow of time in our universe must reverse in scales of order a Hubble time. We find that due to the dynamics of gravity and nonlocal entanglement, a finite size system such as a DeSitter patch with horizon size $H_0^{-1}$ has a finite lifetime $\Delta t$. This phenomenon arises from the dynamic gravitational instabilities that develop during a DeSitter epoch and turn catastrophic. A reversed arrow of time is clearly in disagreement with observations. Thus we are led to conclude: Nature forbids a fundamental $\Lambda$. Or else general relativity must be modified in the IR regime when $\Lambda$ dominates the expansion of the Universe.

2025

This article presents a cosmological model that regards the universe as a whole system. From this perspective, each transformation of the cosmic state constitutes a fundamental measure of time, defined as "cosmic time" or "global time". At the same time, the physical process of cosmic evolution is characterized by the tendency of energy distribution to become more uniform in space — a process that corresponds to the increase of entropy. In this way, a mirror-like relationship is established between cosmic time and cosmic entropy: the direction of time’s flow is determined by the direction of entropy increase, while entropy changes are driven by the dynamic process of energy conduction and distribution. The model further suggests that even in the vacuum, mechanisms of energy conduction remain active, allowing entropy to continuously increase. This supports the universality of the Second Law of Thermodynamics at the cosmic scale. The propagation of electromagnetic and gravitational waves through the vacuum is interpreted as energy conduction through the SEQ (Space Elementary Quanta) network, further validating the effectiveness of entropy increase in vacuum conditions. By integrating thermodynamic time with cosmic time within a causal evolutionary framework, this model provides a new theoretical foundation for understanding the global evolution of the universe, the nature of time, and the universality of entropy.

2009

It is a remarkable fact that all processes occurring in the observable Universe are irreversible, whereas the equations in which the laws of physics are formulated are invariant under time reversal. The emergency of irreversibility from the fundamental laws has been a topic of consideration by physicists, astronomers and philosophers since Boltzmann's formulation of the "H" theorem. In this paper I shall discuss several aspects of this problem and its connection with the dynamics of space-time, within the framework of modern cosmology. I shall comment, briefly, on the nature of physical time and its relation with the so-called "consciousness".

2014

Many thermodynamic processes are irreversible: ice melts in warm water but never spontaneously freezes out of warm water, air leaks out of a pressurized bicycle tire but never leaks back in, and so on. The Second Law of Thermodynamics provides a highlevel explanation for these temporal asymmetries, but a satisfactory explanation in terms of more fundamental laws has been notoriously elusive. I defend a cosmological explanation, according to which the temporal asymmetry of thermodynamics derives ultimately from an asymmetry in the boundary conditions of the universe-namely, the fact that the distribution of mass was quite different at the beginning of the universe than it will be at the end. Recently, three formidable objections have been raised against this cosmological