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The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…

Cosmic inflation claims to make the initial conditions of the standard big bang "generic". But Boltzmann taught us that the thermodynamic arrow of time arises from very non-generic ("low entropy") initial conditions. I discuss how to…

This paper investigates the influence of extra dimensions on the nature of the arrow of time. We demonstrate that the observed arrow of time can be explained by the monotonic growth of the multidimensional manifold's volume. Unlike…

We present a novel solution to the low entropy and arrow of time puzzles of the initial state of the Universe. Our approach derives from the physics of a specific generalization of Matrix theory put forth in earlier work as the basis for a…

We present an exact relationship between the entropy production and the distinguishability of a process from its time-reverse, quantified by the relative entropy between forward and backward states. The relationship is shown to remain valid…

We show that the Wheeler-DeWitt equation with a consistent boundary condition is only compatible with an arrow of time that formally reverses in a recollapsing universe. Consistency of these opposite arrows is facilitated by quantum effects…

In this paper, we investigate an important issue addressed by several approaches to quantum cosmology, like that based on loop quantum gravity and string theory: the existence of an arrow of time driving the cosmological evolution according…

The problem of time is a deep paradox in our physical description of the world. According to Aristotle's relational theory, time is a measure of change and does not exist on its own. In contrast, quantum mechanics, just like Newtonian…

The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws…

In the understanding of the fundamental interactions, the origin of an arrow of time is viewed as problematic. However, quantum field theory has an arrow of causality, which tells us which time direction is the past lightcone and which is…

The existence of a thermodynamic arrow of time in the present universe implies that the initial state of the observable portion of our universe at (or near) the ``big bang'' must have been very ``special''. We argue that it is not plausible…

Fundamental interactions are either fully or nearly symmetric under time reversal. But macroscopic phenomena have a definite arrow of time. Though there is no convergence on the origin of time's preferential direction, many researchers…

The second law of thermodynamics states that the entropy of an isolated system can only increase over time. This appears to conflict with the reversible evolution of isolated quantum systems under the Schr\"odinger equation, which preserves…

While the basic laws of physics seem time-reversal invariant, our understanding of the apparent irreversibility of the macroscopic world is well grounded in the notion of entropy. Because astrophysics deals with the largest structures in…

Our observed Universe has a very strong arrow of time rooted in its low entropy starting point. This low entropy start can be related to various "tuning puzzles" about the early state of the Universe. Here we explore the relationship…

How does the arrow of time (dissipative, irreversible behavior) emerge from time-reversible Hamiltonian mechanics? Two ingredients are needed: the underlying system must be ergodic or phase-mixing, and our knowledge of the system must be…

In this paper we discuss the traditional approaches to the problem of the arrow of time. On the basis of this discussion we adopt a global and non-entropic approach, according to which the arrow of time has a global origin and is an…

This is the first of five papers comprising The Semantic Arrow of Time. The argument begins with a claim: computing's arrow of time is semantic, not thermodynamic. The direction in which meaning is preserved or destroyed across transactions…

Understanding the emergence of the thermodynamic arrow of time in microscopic systems is of fundamental importance, particularly given that unitary evolution preserves time-reversal symmetry. While projective measurements introduce temporal…

Based on the hypothesis that the thermodynamic arrow of time is an emergent phenomenon of quantum state complexity evolution, we further propose that the natural pace of time flow is proportional to the changing rate of quantum state…