The Thermodynamic Cost of Computing with Heat
Abstract
Autonomous quantum thermal machines have recently been proposed as physics-based computing substrates where logical inputs and outputs are encoded in temperature gradients. While such ``thermodynamic neurons'' exhibit a clear trade-off between computational fidelity and heat dissipation, the fundamental information-theoretic limits of temperature-encoded computation remain uncharacterized. Here, we derive rigorous bounds linking average error probability, channel capacity, and entropy production for finite-capacity thermal reservoirs operating far from equilibrium. We prove that the minimal dissipation required to achieve a target average error probability ⟨ ξ⟩ diverges as ⟨ ξ⟩ approaches a fundamental minimum error floor epsMin imposed by finite-reservoir thermal fluctuations. We further establish a thermodynamic channel capacity that saturates at high dissipation, and quantify the minimal dissipation required for cascaded networks to maintain target fidelity. We demonstrate that the required dissipation grows linearly 𝒪(L) with network depth for shallow networks, but diverges as the network depth L approaches a fundamental maximum limit Lmax = epsNet/epsMin imposed by the minimum error floor. Furthermore, under strong noise amplification conditions, the required dissipation can grow up to 𝒪(L3). Our framework bridges stochastic thermodynamics, finite-time information theory, and autonomous computation, providing rigorous design principles for energy-efficient analog thermodynamic hardware.
Versions
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BibTeX
@misc{almasri2026thermodynamic,
title = {{The Thermodynamic Cost of Computing with Heat}},
author = {M. W. AlMasri},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.10027},
eprint = {2608.10027},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10027},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - The Thermodynamic Cost of Computing with Heat
AU - M. W. AlMasri
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2608.10027
UR - https://arxiv.org/abs/2608.10027
AB - Autonomous quantum thermal machines have recently been proposed as physics-based computing substrates where logical inputs and outputs are encoded in temperature gradients. While such ``thermodynamic neurons'' exhibit a clear trade-off between computational fidelity and heat dissipation, the fundamental information-theoretic limits of temperature-encoded computation remain uncharacterized. Here, we derive rigorous bounds linking average error probability, channel capacity, and entropy production for finite-capacity thermal reservoirs operating far from equilibrium. We prove that the minimal dissipation required to achieve a target average error probability ⟨ ξ⟩ diverges as ⟨ ξ⟩ approaches a fundamental minimum error floor epsMin imposed by finite-reservoir thermal fluctuations. We further establish a thermodynamic channel capacity that saturates at high dissipation, and quantify the minimal dissipation required for cascaded networks to maintain target fidelity. We demonstrate that the required dissipation grows linearly 𝒪(L) with network depth for shallow networks, but diverges as the network depth L approaches a fundamental maximum limit L_max = epsNet/epsMin imposed by the minimum error floor. Furthermore, under strong noise amplification conditions, the required dissipation can grow up to 𝒪(L^3). Our framework bridges stochastic thermodynamics, finite-time information theory, and autonomous computation, providing rigorous design principles for energy-efficient analog thermodynamic hardware.
ER -