Time's Second Arrow
Clara Peeters, A Bouquet of Flowers, ca. 1612. European Paintings, The Metropolitan Museum of Art.
Purchase, Lila Acheson Wallace, Howard S. and Nancy Marks, Friends of European Paintings, and Mr. and Mrs. J. Tomilson Hill Gifts, Gift of Humanities Fund Inc., by exchange, Henry and Lucy Moses Fund Inc. Gift, and funds from various donors, 2020 (2020.22).What is this mysterious, fleeting phenomenon that we experience as “now”?
For better or worse, we remember the past, but we can never remember what is yet to be.
No one escapes time’s arrow. An incessant drive toward disorder and decay fills our lives. In its most quotidian manifestations, it dictates that our new shoes eventually become scuffed, our new car dinged. Likewise, the arrow of time points our fragile bodies on an inexorable path of decline, death, and decay. Moments that have passed are irreversible. That terrible thing you said—the one you wish could be unsaid—is beyond unsaying.
In the canon of existing natural laws, only one statement—the second law of thermodynamics—embeds a direction to time, and it declares that “the disorder of a closed system must increase.” Entropy will have its way.
Yet in your heart and mind, you know that such a dispiriting framing cannot be the complete story of nature’s ever-changing face. After all, the universe started almost 14 billion years ago with the Big Bang—a time when there were no atoms or molecules, no planets or stars, no people nor any books for them to read.
Look around you today at the pervasive wonders of our world: Flowers bloom, birds sing, rainbows grace the luminous sky. We watch in awe as our children are born, grow, and learn. From wordless beginnings, humans have created poetry, art, music, and science. Everywhere we look, miraculous order emerges and novel patterns form.
These shared human experiences reveal an obvious truth. There must be a missing law of nature—one that speaks to how the universe trends toward such remarkable states of intricate organization and flamboyant behavior.
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We live in a cosmos of impartial, immutable, universal order. Every action has a cause. Every desire, every ambition is constrained by natural law.
Nature’s laws exist at varied scales of space and time, with many phenomena lying far beyond our five senses. We do not directly experience the counterintuitive, atomic-scale quantum world. Travelers of our generations will never encounter the strange behaviors of objects moving close to the speed of light. Similarly, the relativistic space-time distortions of masses large enough to create black holes are far beyond anything we can imagine. Modern physics has made astonishing technological progress in extending our senses to probe such unfamiliar realms. Patterns of strange, yet lawful, behavior continue to emerge from such investigations, but these extreme environments play almost no perceptible role in our day-to-day lives.
Rather, our everyday concerns are addressed by the macroscopic natural laws—the behaviors of matter, energy, forces, and motions at the familiar scales of time and space that frame human experience. Why do objects move? How does gravity hold us to Earth? What are heat and light? When did life emerge, and how has it evolved? These are the questions that affect us every day of our lives. It is little wonder, then, that we so desperately seek universal, predictive laws that describe and explain what we experience firsthand—the natural laws that dictate what we can and cannot do in a physical universe.
Each law of nature describes and explains a constellation of related phenomena. They enable sound predictions of what might be, as well as sobering reminders of what can never be.
So, are we done? Can we close the books on discovering these natural laws? We think not. We think science has missed something obvious—because increasing disorder is not the only aspect of the cosmos that changes with time.
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Cosmic evolution began at an instant of time—a moment of creation 13.8 billion years ago when everything that defines our universe appeared, seemingly out of nothing. All matter and energy simply became. The nascent cosmos was compressed into a volume so small that all forces, mass, and energy were homogenized into an incomprehensibly hot, dense dot.
No stars or planets arose at that early stage, and nothing resembling what we think of as the universe evolved for a very long time. Everything existed as a soup so scalding that positively charged nuclei and negatively charged electrons couldn’t bind to form atoms. It was far too hot, far too chaotic, for order to arise.
The next half-million years saw the cosmos rapidly expand and cool. Once protons and electrons slowed down enough for atoms to form, the photons of light could finally wander freely. We see the vestiges of this primordial light as a faint glow of microwave radiation that permeates the universe today, telling the story of the moment when atoms, almost all of them hydrogen or helium (the first two elements of the periodic table), emerged some 400,000 years after the Big Bang. Only then could gravity begin to lump atoms together to make the first generation of stars—the engines of atomic evolution.
At the Big Bang’s moment of creation, the universe was featureless. Yet generation after generation of novelty ensued. Atoms and molecules, stars and planets, oceans and atmospheres, rocks and minerals, life and language, and much more have sequentially graced the cosmos. Even as cosmic disorder inevitably has had its way, the universe has evolved and continues to evolve.
Our lives mirror this temporal dichotomy. Yes, we get sick and grow older. All of us must die and our bodies will inexorably fragment, disordering into a vast collection of molecular bits. Yet we also experience countless examples of increasing order: stars shine, crystals grow, seeds sprout. Humans create language, music, art, and science. Must not nature’s laws echo what all of us experience and know to be true?
We propose that nature reveals an as yet uncodified law of increasing order—a second arrow of time. This missing law must describe and explain the universal tendency for certain systems to display increases in order—to become more interesting, even as the disorder of the surrounding universe increases.
Generations of previous scientists have suggested that such wonders are simply quirks of a single arrow of time in a universe that is racing to increase entropy as fast as possible. By one extreme version of this disheartening interpretation, our energy-consuming human brains have evolved as an especially efficient way to radiate waste heat into the depths of space.
We disagree. We counter that the breathtaking transformations from atoms to stars to planets to life—what has been called cosmic evolution—are manifestations of a universal imperative that has been at play since the Big Bang.
Why does biological evolution continually produce new richness, rather than solve for the most optimal solution and call it a day? The answer is that Earth is complexly dynamic, and life itself compounds that complexity. The functional landscape that life must navigate is not only rugged, with many precipices and false summits, but also changing in time.
The law of increasing entropy applies to all possible configurations with equal weight, but nature embraces some configurations while rejecting others. While dissipation of energy must accompany any change in the evolving system, that dispersion of energy into space and the accompanying increase in entropy cannot completely describe, much less explain, how many complex evolving systems come into being in the first place. Nor can those laws predict how they will change going forward.
Functional information offers a powerful way to compare evolving systems in which only a tiny fraction of all possible configurations displays a desired function. Throughout the course of natural selection, it is functional information, not entropy, that describes how the system will change. And here we glimpse a possible path forward in our quest for a missing law of evolution: What if evolution obeys a law of increasing functional information? That increase would represent a second arrow of time—an arrow of increasing localized order and complexity. If our conjecture is correct, then time’s second arrow is completely consistent with entropy’s increasing universal disorder, but it is a different and independent phenomenon.
In a variegated environment, there’s always something new to learn. It pays to be able to predict changes, to find new resources, and to develop new ways of being. Over generational time, Darwinian evolution produces recipes of success written in genetic code. But it’s also a slow and wasteful endeavor. So, life evolved faster ways to sense and transmit information about its environment. Life on Earth has burst into a dizzying array of being and becoming, but the thread of information ties you and every living thing around you back to our humble beginnings. You carry within you the ultimate molecular memory that was forged into existence at the origin of life. A memory of persistence. A memory of replication. A memory of novelty.
Leading cosmological models predict that in some 10100 years, give or take a few zeros, our ever-expanding universe will approach a so-called heat death, cooling indefinitely into the depths of time. At this point, the universe will be near its maximum-entropy state. All conceivable reserves of useful energy will be spent, curtailing combinatorial exploration.
Nevertheless, thinking about our cosmological bookends—the universe’s scalding birth, too chaotic for order to emerge, and the universe’s frigid fate, too inert and uniform to produce complexity—gifts us a profound perspective on the present: Cherish today, for we truly belong to the interesting part of cosmic history, a middle age in which the law of increasing functional information manifests in a most dazzling array of phenomena, including ourselves.
Time’s arrow of increasing information gives all of us a degree of agency—the chance to select our favored path in life, as we move, every day, through varying states of harmony and decay. In this way, the law of increasing functional information could be seen as a law of hope. ♦
Adapted from Time's Second Arrow: Evolution, Order, and a New Law of Nature. Copyright (c) 2026 by Robert M. Hazen and Michael Ling-Jun Wong. Used with permission of the publisher, W. W. Norton & Company, Inc. All rights reserved.
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