A Heuristic Study of Temperature: Quantum Circuitry in Thermal Systems

TL;DR

This paper introduces Complexity Window Thermodynamics (CWT), a new framework that models thermodynamic singularities through computational complexity constraints, linking thermodynamics, quantum computation, and gravity.

Contribution

It proposes CWT, a novel approach that incorporates complexity limits into thermodynamics, smoothing singularities and unifying concepts across physics and computation.

Findings

CWT smooths out classical thermodynamic singularities.

Derives a generalized First Law driven by complexity.

Suggests universe's complexity is comparable to holographic entropy.

Abstract

The singularities prevalent in classical thermodynamics largely stem from the "postulate of equal a priori probabilities" neglecting the physical constraints imposed by computational complexity. This paper introduces Complexity Window Thermodynamics (CWT), a framework that characterizes the observer's "ignorance" via a finite complexity budget, thereby naturally smoothing out singular behaviors associated with phase transitions and negative temperatures within this window. We derive a generalized First Law of Thermodynamics driven by a complexity generation potential, which incorporates "information processing work," and demonstrate a universal action-time bound constraining the growth of complexity. CWT not only offers a unified perspective on critical phenomena in condensed matter and the black hole information problem but also suggests that the total generatable complexity of the universe is comparable in order of magnitude to its holographic entropy. Thus, it paves a new pathway for a resource-theoretic unification of thermodynamics, quantum computation, and gravity.