arXiv subjects

Guo-Hua Xu

Publications and source records attributed to Guo-Hua Xu.

6 recordsLinked to original sources

arXiv2026

Unified geometric formalism for dissipation and its fluctuations in finite-time microscopic heat engines

Microscopic heat engines operate in regimes where thermodynamic quantities fluctuate strongly, making stochastic effects an essential aspect of their performance. However, existing geometric formulations of finite-time thermodynamics primarily characterize average dissipation and do not systematically capture its fluctuations. Here, we develop a unified geometric framework that consistently describes both the mean dissipated availability and its fluctuations. In the linear-response regime, we show that these quantities are governed by metric tensors constructed from equilibrium correlation functions, providing a common geometric structure for dissipation and its fluctuations. This framework yields geometric bounds on both the mean and variance of the dissipated availability, and thereby on the efficiency and its fluctuations. The formalism applies broadly to stochastic systems, including Markov jump processes and overdamped and underdamped Brownian dynamics, establishing a unified geometric description across microscopic heat engines.

cond-mat.stat-mech↗

arXiv2025

Thermodynamic Geometric Constraint on the Spectrum of Markov Rate Matrices

The spectrum of Markov generators encodes physical information beyond simple decay and oscillation, which reflects irreversibility and governs the structure of correlation functions. In this work, we prove an ellipse theorem that provides a universal thermodynamic geometric constraint on the spectrum of Markov rate matrices. The theorem states that all eigenvalues lie within a specific ellipse in the complex plane. In particular, the imaginary parts of the spectrum, which indicate oscillatory modes, are bounded by the maximum thermodynamic force associated with individual transitions. This spectral bound further constrains the initial short-time behavior of correlation functions between two arbitrary observables. Finally, we compare our result with a previously proposed conjecture, which remains an open problem and warrants further investigation.

cond-mat.stat-mech↗

arXiv2025

Universal relations and bounds for fluctuations in quasistatic small heat engines

The efficiency of any heat engine, defined as the ratio of average work output to heat input, is bounded by Carnot's celebrated result. However, this measure is insufficient to characterize the properties of miniaturized heat engines carrying non-negligible fluctuations, and a study of higher-order statistics of their energy exchanges is required. Here, we generalize Carnot's result for reversible cycles to arbitrary order moment of the work and heat fluctuations. Our results show that, in the quasistatic limit, higher-order statistics of a small engine's energetics depend solely on the ratio between the temperatures of the thermal baths. We further prove that our result for the second moment gives universal bounds for the ratio between the variances of work and heat for quasistatic cycles. We test this theory with our previous experimental results of a Brownian Carnot engine and observe the consistency between them, even beyond the quasistatic regime. Our results can be exploited in the design of thermal nanomachines to reduce their fluctuations of work output without marginalizing its average value and efficiency.

cond-mat.stat-mech↗

arXiv2025

Dephasing Enabled Fast Charging of Quantum Batteries

We propose and analyze a universal method to obtain fast charging of a quantum battery by a driven charger system using controlled, pure dephasing of the charger. While the battery displays coherent underdamped oscillations of energy for weak charger dephasing, the quantum Zeno freezing of the charger energy at high dephasing suppresses the rate of transfer of energy to the battery. Choosing an optimum dephasing rate between the regimes leads to a fast charging of the battery. We illustrate our results with the charger and battery modeled by either two-level systems or harmonic oscillators. Apart from the fast charging, the dephasing also renders the charging performance more robust to detuning between the charger, drive, and battery frequencies for the two-level systems case.

quant-ph↗

arXiv2022

Relation between fluctuations and efficiency at maximum power for small heat engines

We study the ratio between the variances of work output and heat input, $η^{(2)}$, for a class of four-stroke heat engines which covers various typical cycles. Recent studies on the upper and lower bounds of $η^{(2)}$ are based on the quasistatic limit and the linear response regime, respectively. We extend these relations to the finite-time regime within the endoreversible approximation. We consider the ratio $η_{\text{MP}}^{(2)}$ at maximum power and find that the square of the Curzon-Ahlborn efficiency, $η_{\text{CA}}^2$, gives a good estimate of $η_{\text{MP}}^{(2)}$ for the class of heat engines considered, i.e., $η_{\text{MP}}^{(2)} \simeq η_{\text{CA}}^2$. This resembles the situation where the Curzon-Ahlborn efficiency gives a good estimate of the efficiency at maximum power for various kinds of finite-time heat engines. Taking an overdamped Brownian particle in a harmonic potential as an example, we can realize such endoreversible small heat engines and give an expression of the cumulants of work output and heat input. The approximate relation $η_{\text{MP}}^{(2)} \simeq η_{\text{CA}}^2$ is verified by numerical simulations. This relation also suggests a trade-off between the efficiency and the stability of finite-time heat engines at maximum power.

cond-mat.stat-mech↗

arXiv2022

Correlation-enhanced Stability of Microscopic Cyclic Heat Engines

For cyclic heat engines operating in a finite cycle period, thermodynamic quantities have intercycle and intracycle correlations. By tuning the driving protocol appropriately, we can get the negative intercycle correlation to reduce the fluctuation of work through multiple cycles, which leads to the enhanced stability compared to the single-cycle operation. Taking the Otto engine with an overdamped Brownian particle as a working substance, we identify a scenario to get such enhanced stability by the intercycle correlation. Furthermore, we demonstrate that the enhancement can be readily realized in the current experiments for a wide range of protocols. By tuning the parameters within the experimentally achievable range, the uncertainty of work can be reduced to below $\sim 50 \%$.

cond-mat.stat-mech↗