The Thermodynamic Cost of Computing with Heat

• URL: http://arxiv.org/abs/2608.10027v1
• Date: Sun, 09 Aug 2026 19:51:57 GMT
• Title: The Thermodynamic Cost of Computing with Heat
• Abstract summary: We prove that the minimal dissipation required to achieve a target average error probability $langle rangle$ diverges as $langle rangle$ approaches a fundamental minimum error floor $epsMin$ imposed by finite-reservoir thermal fluctuations.<n>Our framework bridges thermodynamics, finite-time information theory, and autonomous computation, providing rigorous design principles for energy-efficient hardware.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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 $\langle ξ\rangle$ diverges as $\langle ξ\rangle$ 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, demonstrating a fundamental $\mathcal{O}(L \ln L)$ overhead with network depth, with the required dissipation growing up to $\mathcal{O}(L^3)$ under strong noise amplification conditions. Our framework bridges stochastic thermodynamics, finite-time information theory, and autonomous computation, providing rigorous design principles for energy-efficient analog thermodynamic hardware.

Related papers

• Quantum annealers as programmable thermal machines [0.0]
  We characterize the D-Wave quantum annealer as a closed thermodynamic cycle.<n>From initial and final Ising energies and an effective temperature fitted to the output distribution, we obtain lower bounds on entropy production, environment energy exchange, work, and power.
  arXiv  Detail & Related papers  (2026-08-05T07:57:20Z)
• On the robustness of noisy solutions in non-convex neural networks [42.548424354574585]
  We show that frozen one-step replica-symmetry-breaking solution densities survive at any finite temperature.<n>We show that dense, algorithmically accessible regions of finite-energy persist beyond $_rm OGP$, up to a threshold $_rm OGP()$ that grows with the allowed error.<n>In the teacher-student setting, we show that these wide, finite-energy regions still retain good generalization.
  arXiv  Detail & Related papers  (2026-07-29T14:57:26Z)
• Fault tolerant computation of the static structure factor and finite size effects [43.936586633107396]
  We develop a quantum post-processing strategy for the leading two-body finite-size correction.<n>After one-body shell effects are reduced by twist averaging, the dominant residual error is controlled by long-wavelength density fluctuations.<n>We also introduce adaptive global and local binary search procedures for identifying the infrared fitting window used to reconstruct the two-body finite size error correction.
  arXiv  Detail & Related papers  (2026-06-26T05:31:08Z)
• SYK thermal expectations are classically easy at any temperature [49.788604174558564]
  We give a simple classical algorithm that approximates thermal expectations.<n>We show it has quasi-polynomial cost $nO(log n/)$ for all temperatures above a phase transition in the free energy.
  arXiv  Detail & Related papers  (2026-02-26T04:48:32Z)
• Thermodynamic significance of QUBO encoding on quantum annealers [0.0]
  We study a Job Shop Scheduling instance using a two- parameter family of encodings controlled by penalty weights.<n>We find that the same encoding transitions that govern computational hardness also reorganize dissipation.<n>Our results establish QUBO penalties as thermodynamic control knobs and motivate thermodynamics-aware encoding strategies for noisy intermediate-scale quantum annealers.
  arXiv  Detail & Related papers  (2026-01-07T21:18:54Z)
• Coherence Dispersion and Temperature Scales in a Quantum-Biology Toy Model [51.56484100374058]
  We investigate how quantum coherence can scatter among the several off-diagonal elements of an arbitrary quantum state.<n>By focusing on out-of-equilibrium systems, we use the developed framework to address a simplified model of cellular energetics.
  arXiv  Detail & Related papers  (2025-12-13T14:21:34Z)
• Thermalization with partial information [0.7673339435080445]
  We find analogous fundamental principles identifying a noisy quantum channel $mathcalT$ to model the system's dynamics.<n>We propose a learning algorithm for quantum channels based on the maximum channel entropy principle.
  arXiv  Detail & Related papers  (2025-08-06T00:52:29Z)
• Erasure cost of a quantum process: A thermodynamic meaning of the dynamical min-entropy [1.1827829754757404]
  We investigate the thermodynamic costs associated with erasing (and preparing) quantum processes.<n>We focus on the adversarial erasure cost of the reduced dynamics.<n>This insight bridges thermodynamics, information theory, and the fundamental limits of quantum computation.
  arXiv  Detail & Related papers  (2025-06-05T17:53:17Z)
• Thermodynamics-Consistent Graph Neural Networks [50.0791489606211]
  We propose excess Gibbs free energy graph neural networks (GE-GNNs) for predicting composition-dependent activity coefficients of binary mixtures. The GE-GNN architecture ensures thermodynamic consistency by predicting the molar excess Gibbs free energy. We demonstrate high accuracy and thermodynamic consistency of the activity coefficient predictions.
  arXiv  Detail & Related papers  (2024-07-08T06:58:56Z)
• A Universal Constraint on Computational Rates in Physical Systems [0.0]
  General proof is given for open quantum systems showing that a computer thermally coupled to its environment will necessarily dissipate entropy (and hence heat) Specifically, a lower bound is obtained that corresponds to the adiabatic regime, in which the amount of entropy dissipated per computational operation is proportional to the rate of computation.
  arXiv  Detail & Related papers  (2022-08-23T21:18:53Z)
• Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
  Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Our results explain finite-time thermalization in chaotic open quantum systems.
  arXiv  Detail & Related papers  (2021-12-14T18:48:31Z)
• Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results [68.8204255655161]
  We show that the proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates.
  arXiv  Detail & Related papers  (2021-05-11T14:08:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.