The second law of thermodynamics says entropy increases. This is not controversial. What is controversial is why it increases, which requires asking why it was ever low to begin with. David Albert's answer is the Past Hypothesis: the universe started in an extraordinarily low-entropy macrostate. Combined with a uniform probability distribution over microstates consistent with that macrostate (Albert calls the package the Mentaculus), this predicts thermodynamic behavior downstream. The problem is that every argument for why the universe started in a low-entropy state turns out to assume a prior that is itself low-entropy. In a 2025 paper, Wolpert, Rovelli, and Scharnhorst identified this as a conditioning-moment problem: you have to pick a moment to condition on, and the choice of that moment already builds in the asymmetry you are trying to explain. The circularity is not a technical mistake. It runs through all standard arguments.
Inflation is the most popular cosmological attempt to derive the low-entropy start rather than just postulate it. It fails in a specific way. The inflaton field, as it rolls down its potential, generates an exponentially expanding region with low-entropy matter distribution. But you still need to explain why the inflaton started in a high-potential, low-entropy state suitable for inflation. Any prior you write down over inflaton field configurations at the Planck epoch is doing the same job as the Past Hypothesis: imposing a boundary condition without deriving it. Inflation displaces the question, it does not answer it. Penrose made the same complaint about his own Weyl curvature hypothesis: positing a low-entropy initial singularity explains the arrow but not why the singularity was that way rather than high-entropy. Huw Price sharpens this into a general argument. In a block universe where past and future are equally real, any asymmetric explanation of the arrow must either assume a primitive temporal asymmetry or import one through an asymmetric boundary condition. There is no third option. Penrose and Percival's attempts to ground the arrow in quantum state reduction have this structure, and Price argues they are circular for exactly this reason.
What the Past Hypothesis does well is locating the explanandum precisely. Before Albert, you could debate the arrow of time in vague terms about causation and memory. The Mentaculus makes the claim specific: the universe's initial macrostate, the Statistical Postulate, and the dynamical laws together predict everything we observe about thermodynamic asymmetry. Subsystem probabilities work correctly within this framework. The failure is not predictive but explanatory: the framework assumes what it sets out to explain. That is not a small thing, but it is a clean thing. An honest posit is better than a circular derivation.
Connections
Landauer's erasure principle connects here in an unexpected direction. If information is physical and erasing it costs energy, then the Past Hypothesis can be read as a maximum-information starting point: the universe began with maximally specific initial conditions, and entropy increase is the dispersal of that specificity into inaccessible correlations. The Boltzmann Brain scenario looks different from this angle. A Boltzmann Brain is not a universe that has spontaneously fluctuated into order from chaos. It is a universe that has already erased its initial specificity and then, by enormous coincidence, formed a local pocket of low entropy. The improbability is the same, but the framing clarifies what is actually needed: not randomness, but a starting condition with very little erasure behind it.
The unresolved thread is quantum unitarity. Unitary evolution conserves information. The thermodynamic arrow, in this picture, is not the destruction of information but its dispersal into entanglement with inaccessible degrees of freedom. The entropy we measure is coarse-grained entropy, not a count of actually destroyed distinctions. This matters because it means the arrow of time, at the fundamental level, may be an artifact of which degrees of freedom we can access rather than a fact about the universe's dynamics. That is the same problem that shows up in black hole evaporation. Whether Hawking radiation is truly thermal or encodes the infalling information is, in a precise sense, the same question as whether the thermodynamic arrow is fundamental or perspectival.
What lingered
The regress problem is not going away. Every cosmological proposal that claims to explain the low-entropy start adds a prior somewhere. The Prior Hypothesis just makes the posit explicit. That honesty is philosophically underrated. Most of the proposals that claim to derive the arrow — inflation, the no-boundary proposal, cyclic cosmologies — are doing the same thing with more steps. The arrow of time may require a primitive asymmetry that no physical theory can derive from symmetric dynamics. If that is right, then the question shifts from “why does time have a direction?” to “what kind of primitive posit are we most willing to accept?” Albert's answer is at least clearly stated.