Bounded thermal weights from a discrete Boltzmann factor

TL;DR

This paper explores a bounded discrete Boltzmann weight's implications for quantum thermodynamics, black hole radiation, and modified dispersion relations, highlighting the effects of a cutoff scale and deviations from continuum physics.

Contribution

It introduces a systematic analysis of the bounded thermal weight, deriving new results for Hawking radiation suppression, Jarzynski-type identities, and kinematic bounds, extending statistical and quantum thermodynamic frameworks.

Findings

Black-hole luminosity is suppressed near the cutoff scale.

An exact Jarzynski-type identity is established for discrete thermal weights.

Laboratory signatures of the bounded model are negligible at universal Planck suppression.

Abstract

The discrete Boltzmann factor $B_E(\beta_n)=(1-bE)^n$, introduced by Chung, Hassanabadi, and Boumali, provides a lattice regularization of the canonical weight $e^{-\beta E}$ and imposes the compact-support condition $E<1/b$. In the present analysis we systematically separate results that follow directly from this bounded thermal weight from those that require additional phenomenological input. First, we study the discrete Bose--Einstein occupation factor relevant for Hawking radiation, derive the leading suppression of black-hole luminosity, and show that the thermal Hawking channel shuts off as the cutoff scale is approached. Second, we formulate a discrete work functional built from ratios of thermal weights and establish an exact Jarzynski-type identity for deterministic measure-preserving protocols; in contrast, the corresponding Crooks relation does not collapse to a function of work alone, and first-order approximations retain an explicit initial-energy dependence that cannot be reduced to a simple $W$-dependent correction without additional assumptions. Third, and purely as an ancillary kinematic extension rather than a derivation from the statistical framework itself, we examine a bounded modified-dispersion ansatz and estimate the associated time-of-flight constraints. Throughout, we include illustrative figures, clarify the non-universal status of the entropy correction, and emphasize that direct laboratory signatures are negligible whenever $b$ is universal and Planck suppressed. Finally, the standard continuum expressions are recovered smoothly in the limit $b\to 0$.