The puzzle of the thermodynamic arrow of time reduces to the question of how the universe could have had lower entropy in the past. I show that no special entropy lowering mechanism (or fluctuation) is necessary. As a consequence of expansion, at a particular epoch in the history of the universe a state that was near maximum entropy under the dominant short range forces becomes extremely unlikely, due to a switchover to newly dominant long range forces. This happened at about the time of decoupling, prior to which I make no statement about arrows. The role of cosmology in thermodynamics was first suggested by T. Gold.
In this paper we lay out an argument that generically the psychological arrow of time should align with the thermodynamic arrow of time where that arrow is well-defined. This argument applies to any physical system that can act as a memory, in the sense of preserving a record of the state of some other system. This result follows from two principles: the robustness of the thermodynamic arrow of time to small perturbations in the state, and the principle that a memory should not have to be fine-tuned to match the state of the system being recorded. This argument applies even if the memory syste…
The mechanism by which thermodynamics sets the direction of time's arrow has long fascinated scientists. Here, we show that a machine learning algorithm can learn to discern the direction of time's arrow when provided with a system's microscopic trajectory as input. The performance of our algorithm matches fundamental bounds predicted by nonequilibrium statistical mechanics. Examination of the algorithm's decision-making process reveals that it discovers the underlying thermodynamic mechanism and the relevant physical observables. Our results indicate that machine learning techniques can be us…
In [Sch05a], it is argued that Boltzmann's intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. [Haw94] presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will…
We investigate a thermodynamic arrow associated with quantum projective measurements in terms of the Jensen-Shannon divergence between the probability distribution of energy change caused by the measurements and its time reversal counterpart. Two physical quantities appear to govern the asymptotic values of the time asymmetry. For an initial equilibrium ensemble prepared at a high temperature, the energy fluctuations determine the convergence of the time asymmetry approaching zero. At low temperatures, finite survival probability of the ground state limits the time asymmetry to be less than $\…
Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of time. We present general qualitative arguments for that cl…
In the joint paper "Bridging the neuroscience and physics of time" Rovelli, as the physicist coauthor of neuroscientist Dean Buonomano, makes statements that rely on theoretical frameworks employed when the laws of thermodynamics and general relativity were discovered. Their reconsideration in the light of subsequent insights suggests growth of entropy is not the origin of time's arrow and that a notion of universal simultaneity may exist within general relativity. This paper is a slightly extended form of my invited contribution to the forthcoming Frontiers in Psychology special issue "Physic…
According to statistical mechanics, micro-states of an isolated physical system (say, a gas in a box) at time $t_0$ in a given macro-state of less-than-maximal entropy typically evolve in such a way that the entropy at time $t$ increases with $|t-t_0|$ in both time directions. In order to account for the observed entropy increase in only one time direction, the thermodynamic arrow of time, one usually appeals to the hypothesis that the initial state of the universe was one of very low entropy. In certain recent models of cosmology, however, no hypothesis about the initial state of the universe…
A profound quest of statistical mechanics is the origin of irreversibility - the arrow of time. New stimulants have been provided, thanks to unprecedented degree of control reached in experiments with isolated quantum systems and rapid theoretical developments of manybody localization in disordered interacting systems. The proposal of (many-body) eigenstate thermalization (ET) for these systems reinforces the common belief that either interaction or extrinsic randomness is required for thermalization. Here, we unveil a quantum thermalization mechanism challenging this belief. We find that, pro…
In both thermodynamics and quantum mechanics the arrow of time is characterized by the statistical likelihood of physical processes. We characterize this arrow of time for the continuous quantum measurement dynamics of a superconducting qubit. By experimentally tracking individual weak measurement trajectories, we compare the path probabilities of forward and backward-in-time evolution to develop an arrow of time statistic associated with measurement dynamics. We compare the statistics of individual trajectories to ensemble properties showing that the measurement dynamics obeys both detailed a…
This paper is a natural continuation of our previous paper arXiv:1011.4173 . We illustrated earlier that in classical Hamilton mechanics, for overwhelming majority of real chaotic macroscopic systems, alignment of their thermodynamic time arrows occurs because of their low interaction. This fact and impossibility to observe entropy decrease at introspection explain the second law of thermodynamics. The situation in quantum mechanics is even a little bit easier: all closed systems of finite volume are periodic or nearly periodic. The proof in quantum mechanics is in many respects similar to the…
We show that the evidence for a local arrow of time, which is equivalent to the entropy production in thermodynamic systems, can be decomposed. In a system with many degrees of freedom, there is a term that arises from the irreversible dynamics of the individual variables, and then a series of non--negative terms contributed by correlations among pairs, triplets, and higher--order combinations of variables. We illustrate this decomposition on simple models of noisy logical computations, and then apply it to the analysis of patterns of neural activity in the retina as it responds to complex dyn…
We start with reviewing the origin of the idea that entropy and the Second Law are associated with the Arrow of Time. We then introduced a new definition of entropy based on Shannons Measure of Information, SMI. The SMI may be defined on any probability distribution, and therefore it is a very general concept. On the other hand entropy is defined on a very special set of probability distributions. More specifically the entropy of a thermodynamic system is related the probability distribution of locations and velocities or momenta of all the particles, which maximized the Shannon Measure of Inf…
Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. Using a nuclear magnetic resonance setup, we measure the nonequilibrium entropy produced in an isolated spin-1/2 system following fast quenches of an external magnetic field and experimentally demonstrate that it is equal to the entropic distance, expressed by the Kullback-Leibler divergen…
The second law of thermodynamics is asymmetric with respect to time as it says that the entropy of the universe must have been lower in the past and will be higher in the future. How this time-asymmetric law arises from the time-symmetric equations of motion has been the subject of extensive discussion in the scientific literature. The currently accepted resolution of the problem is to assume that the universe began in a low entropy state for an unknown reason. But the probability of this happening by chance is exceedingly small, if all microstates are assigned equal a-priori probabilities. In…
Why does time appear to pass irreversibly? To investigate, we introduce a class of partitioned cellular automata (PCAs) whose cellwise evolution is based on the chaotic baker's map. After imposing a suitable initial condition and restricting to a macroscopic view, we are left with a stochastic PCA (SPCA). When the underlying PCA's dynamics are reversible, the corresponding SPCA serves as a model of emergent time-reversal asymmetry. Specifically, we prove that its transition probabilities are homogeneous in space and time, as well as Markov relative to a Pearlean causal graph with timelike futu…
Strong shockwaves generate entropy quickly and locally. The Newton-Hamilton equations of motion, which underly the dynamics, are perfectly time-reversible. How do they generate the irreversible shock entropy? What are the symptoms of this irreversibility? We investigate these questions using Levesque and Verlet's bit-reversible algorithm. In this way we can generate an entirely imaginary past consistent with the irreversibility observed in the present. We use Runge-Kutta integration to analyze the local Lyapunov instability of the forward and backward processes so as to identify those particle…
Living systems are fundamentally irreversible, breaking detailed balance and establishing an arrow of time. But how does the evident arrow of time for a whole system arise from the interactions among its multiple elements? We show that the local evidence for the arrow of time, which is the entropy production for thermodynamic systems, can be decomposed. First, it can be split into two components: an independent term reflecting the dynamics of individual elements and an interaction term driven by the dependencies among elements. Adapting tools from non--equilibrium physics, we further decompose…
We present non equilibrium molecular dynamics experiments of the unfolding and refolding of an alanine decapeptide in vacuo subject to a Nose-Hoover thermostat. Forward (unfolding) and reverse (refolding) work distribution are numerically calculated for various duration times of the non equilibrium experiments. Crooks theorem is accurately verified for all non equilibrium regimes and the time asymmetry of the process is measured using the recently proposed Jensen-Shannon divergence [E.H. Fend, G. Crooks, Phys. Rev. Lett, 101, 090602] . Results on the alanine decapeptide are found similar to re…
Thermodynamics has a clear arrow of time, characterized by the irreversible approach to equilibrium. This stands in contrast to the laws of microscopic theories, which are invariant under time-reversal. Foundational discussions of this "problem of irreversibility" often focus on historical considerations, and do therefore not take results of modern physical research on this topic into account. In this article, I will close this gap by studying the implications of dynamical density functional theory (DDFT), a central method of modern nonequilibrium statistical mechanics not previously considere…
The second law of thermodynamics states that for a thermally isolated system entropy never decreases. Most physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger than microscopic molecular collision scales and thus can be considered as in local equilibrium. For a many-body system in local equilibrium a stronger version of the second law applies which says that the entropy production at each spacetime point should be non-negative. In this paper we provide a proof of the second law for such systems and a first derivation …
Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing the thermodynamic arrow of time. We study the time development of such fluctuations, especially the very large fluctuations relevant to cosmology. Under fairly general assumptions, the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium. We use this idea to elucidate th…
We demonstrate that irreversibility arises from the principle of microscopic reversibility and the presence of memory in the time evolution of a single copy of a system driven by a protocol. We introduce microscopic reversibility by using the concept of protocol- and pathway-dependent thermodynamic function, as defined in J.R. Arias-Gonzalez, arXiv:1511.08017 [cond-mat.stat-mech], and memory by using the concept of non-Markovianity, as in J.R. Arias-Gonzalez, arXiv:1511.06139 [cond-mat.stat-mech]. We define work as the change in free energy and heat as the change in entropy for micoscopic, ind…
