The Arrow of Time: What Thermodynamics Doesn’t Tell You

Many people think the arrow of time can be explained by the increase of entropy; but that’s inadequate. We’ll explore why.

The irreversibility of time is ubiquitous, but it’s not so obvious why that has to be the case (Photo by Aron Visuals)

Thermodynamics: An Effective Approximation

Thermodynamics has one essential assumption:

Thermodynamics approximates a system using random processes and statistics.

Thermodynamics approximates dynamics of physical systems as random rolling of dice (by Riho Kroll)
  1. Unlucky numbers: 1, 2, 3, 4

The Arrow of Time: A Thermodynamic Explanation

So why does entropy have to increase? Well, since a measurement is akin to rolling the die once, the result is more likely to be a high-entropy state (e.g., unlucky numbers). In particular, if the number of sides of the die is increasing as time goes on, then gradually the entropy of the system (defined by the entropy of the category that it is in) will always tend to increase. In other words:

An increase in entropy is equivalent to the shift from a lucky roll to an unlucky roll

So in this view, the increase of entropy is critically dependent on the fact that our system was previously in a low-entropy state, so that there is room to move to a higher-entropy state! Otherwise, the system wouldn’t change in the first place.

The number of explorable states for the system was smaller in the beginning than in the end.

Entropy’s increase is then ultimately tied to the (apparent) gradual increase of the number of explorable states. Of course, all of this discussion will be vacuous if we cannot explain how non-random physical processes can be approximated by random ones. In the end, a complete explanation for the arrow of time needs to go beyond thermodynamics.

Epilogue: Looking Beyond

To complete the thermodynamic explanation, we must answer two more questions:

  1. Why does the number of states available for exploration get smaller as we travel further back in time?
  1. The initial conditions of the universe (near the Big Bang) are ultimately responsible for the seemingly smaller number of explorable states at the beginning of time

Data Scientist @ LiveRamp | ex Particle Physics Postdoc @ Berkeley | Podcast host @

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