Preprints

We introduce a theoretical framework linking computational complexity to thermodynamic energy costs, proving that quantum algorithmic speedups translate into measurable physical energy savings. Four theorems with computational validation and testable experimental predictions for current quantum platforms bridge Maxwell's demon research with modern quantum information science.

This work proves how quickly the energy cost of a computation approaches its theoretical minimum, known as the Landauer limit. The convergence rate is shown to be optimal and structurally analogous to Shannon's channel coding theorem. A fundamental trade-off between energy, time, and memory is established. Numerical validation confirms the predictions.

This paper proves that holographic systems—where gravity encodes vast amounts of information geometrically—require exponentially fewer resources to describe thermodynamic processes such as cooling than conventional systems of equivalent size. The geometric encoding compresses description costs, though it does not accelerate individual operations.

This paper establishes a duality between quantum measurement and erasure at the level of quantum channels. The authors prove it is uniquely determined by five physical axioms and derive an exact thermodynamic identity: the minimum work cost of a measurement-erasure cycle depends only on the system's dimension and temperature.

Quantum computers must correct errors constantly, each cycle unavoidably dissipating energy. This work derives exact thermodynamic results for that cost in stabilizer codes. Across eleven codes and four platforms, current hardware operates five to eleven orders of magnitude above the fundamental limit, with control and readout as the dominant source.

This work develops a mathematical framework showing that natural selection in energy-scarce environments drives organisms toward the minimum energy cost of computation. It predicts that deep subsurface bacteria, isolated for hundreds of millions of years under energy limitation, may already operate near this bound. Five falsifiable experimental predictions are provided.

This work proposes modeling brain activity using tensor networks, mathematical structures from quantum information theory. Cortical hierarchies are hypothesized to admit a multi-scale network description. The framework defines a quantifiable information-capacity parameter, hypothesized to correlate with consciousness states, and generates experimentally testable predictions.

This paper develops a thermodynamic theory for the space of proofs certifying that a random Boolean formula has no solution. Unlike the solution landscape, which fragments into exponentially many clusters, the proof landscape remains structurally simple at every finite temperature. This simplicity reveals a hidden hierarchy—the entropy ladder—a monotone chain ordered by the restrictiveness of the allowed logical operations, that unifies principal unconditional lower bounds on computational hardness.