arXiv subjects

Yu-Han Ma

Publications and source records attributed to Yu-Han Ma.

At least 37 records · Page 2Linked to original sources

arXiv2023

Engineering Ratchet-Based Particle Separation via Shortcuts to Isothermality

Microscopic particle separation plays vital role in various scientific and industrial domains. In this Letter, we propose a universal non-equilibrium thermodynamic approach, employing the concept of Shortcuts to Isothermality, to realize controllable separation of overdamped Brownian particles. By utilizing a designed ratchet potential with temporal period $τ$, we find in the slow-driving regime that the average particle velocity $\Bar{v}_s\propto\left(1-D/D^*\right)τ^{-1}$, indicating that particles with different diffusion coefficients $D$ can be guided to move in distinct directions with a preset $D^*$. Furthermore, we reveal that there exists an extra energetic cost with a lower bound $W_{\rm{ex}}^{(\rm{min})}\propto\mathcal{L}^{2}\Bar{v}_s$, alongside a quasi-static work consumption. Here, $\mathcal{L}$ is the thermodynamic length of the driving loop in the parametric space. We numerically validate our theoretical findings and illustrate the optimal separation protocol (associated with $W_{\rm{ex}}^{(\rm{min})}$) with a sawtooth potential. This study establishes a bridge between thermodynamic process engineering and particle separation, paving the way for further explorations of thermodynamic constrains and optimal control in ratchet-based particle separation.

cond-mat.stat-mech↗

arXiv2023

Temperature fluctuations in mesoscopic systems

We study temperature fluctuations in mesoscopic $N$-body systems undergoing non-equilibrium processes from the perspective of stochastic thermodynamics. By introducing a stochastic differential equation, we describe the evolution of the system's temperature during an isothermal process, with the noise term accounting for finite-size effects arising from random energy transfer between the system and the reservoir. Our analysis reveals that these fluctuations make the extensive quantities (in the thermodynamic limit) deviate from being extensive for consistency with the theory of equilibrium fluctuation. Moreover, we derive finite-size corrections to the Jarzynski equality, providing insights into how heat capacity influences such corrections. Also, our results indicate a possible violation of the principle of maximum work by an amount proportional to $N^{-1}$. Additionally, we examine the impact of temperature fluctuations in a finite-size quasi-static Carnot engine. We show that irreversible entropy production resulting from the temperature fluctuations of the working substance diminishes the average efficiency of the cycle as $η_{\rm{C}}-\left\langle η\right\rangle \sim N^{-1}$, highlighting the unattainability of the Carnot efficiency $η_{\rm{C}}$ for mesoscopic-scale heat engines even under the quasi-static limit

cond-mat.stat-mech↗

arXiv2023

Finite-Time Optimization of Quantum Szilard heat engine

We propose a finite-time quantum Szilard engine (QSE) with a quantum particle with spin as the working substance (WS) to accelerate the operation of information engines. We introduce a Maxwell's demon (MD) to probe the spin state within a finite measurement time $t_{\rm M}$ to capture the which-way information of the particle, quantified by the mutual information $I(t_{\rm{M}})$ between WS and MD. We establish that the efficiency $η$ of QSE is bounded by $η\leq1-(1-η_{\rm{C}}){\rm ln}2/I(t_{\rm M})$, where $I(t_{\rm M})/\rm{ln}2$ characterizes the ideality of quantum measurement, and approaches $1$ for the Carnot efficiency reached under ideal measurement in quasi-static regime. We find that the power of QSE scales as $P\propto t_{\rm M}^{3}$ in the short-time regime and as $P\propto t_{\rm M}^{-1}$ in the long-time regime. Additionally, considering the energy cost for erasing the MD's memory required by Landauer's principle, there exists a threshold time that guarantees QSE to output positive work.

quant-ph↗

arXiv2022

Experimental implementation of finite-time Carnot cycle

The Carnot cycle is a prototype of ideal heat engine to draw mechanical energy from the heat flux between two thermal baths with the maximum efficiency, dubbed as the Carnot efficiency $η_{\mathrm{C}}$. Such efficiency can only be reached by thermodynamical equilibrium processes with infinite time, accompanied unavoidably with vanishing power - energy output per unit time. In real-world applications, the quest to acquire high power leads to an open question whether a fundamental maximum efficiency exists for finite-time heat engines with given power. We experimentally implement a finite-time Carnot cycle with sealed dry air as working substance and verify the existence of a tradeoff relation between power and efficiency. Efficiency up to $(0.524\pm0.034)η_{\mathrm{C}}$ is reached for the engine to generate the maximum power, consistent with the theoretical prediction $η_{\mathrm{C}}/2$. Our results shall provide a new platform for studying finite-time thermodynamics consisting of nonequilibrium processes.

cond-mat.stat-mech↗

arXiv2022

Simple realization of the polytropic process with a finite-sized reservoir

In many textbooks of thermodynamics, the polytropic process is usually introduced by defining its process equation rather than analyzing its actual origin. We realize a polytropic process of an ideal gas system when it is thermally contact with a reservoir whose heat capacity is a constant. This model can deepen students' understanding of typical thermodynamic processes, such as isothermal and adiabatic processes, in the teaching of thermodynamics. Moreover, it can inspire students to explore some interesting phenomena caused by the finiteness of the reservoir. The experimental implementation of the proposed model with realistic parameters is also discussed.

cond-mat.stat-mech↗

arXiv2022

Dark Information in Black Hole with $λφ$ Fluid

It has been shown that the nonthermal spectrum of Hawking radiation will lead to information-carrying correlations between emitted particles in the radiation. The mutual information carried by such correlations can not be locally observed and hence is dark. With dark information, the black hole information is conserved. In this paper, we look for the spherically symmetric black hole solution in a $λφ$ fluid model and investigate the radiation spectrum and dark information of the black hole. The spacetime structure of this black hole is similar to that of the Schwarzschild one, while its horizon radius is decreased by the $λφ$ fluid. By using the statistical mechanical method, the nonthermal radiation spectrum is calculated. This radiation spectrum is very different from the Schwarzschild case at its last stage because of the effect of the $λφ$ fluid. The $λφ$ fluid reduces the lifetime of the black hole, but increases the dark information of the Hawking radiation.

gr-qc↗

arXiv2021

Minimal Energy Cost to Initialize a Quantum Bit with Tolerable Error

Landauer's principle imposes a fundamental limit on the energy cost to perfectly initialize a classical bit, which is only reached under the ideal operation with infinite-long time. The question on the cost in the practical operation for a quantum bit (qubit) has been posted under the constraint by the finiteness of operation time. We discover a raise-up of energy cost by $\mathcal{L}^{2}(ε)/τ$ from the Landaeur's limit ($k_{B}T\ln2$) for a finite-time $τ$ initialization with an error probability $ε$. The thermodynamic length $\mathcal{L}(ε)$ between the states before and after initializing in the parametric space increases monotonously as the error decreases. For example, in the constant dissipation coefficient ($γ_{0}$) case, the minimal additional cost is $0.997k_{B}T/(γ_{0}τ)$ for $ε=1\%$ and $1.288k_{B}T/(γ_{0}τ)$ for $ε=0.1\%$. Furthermore, the optimal protocol to reach the bound of minimal energy cost is proposed for the qubit initialization realized via a finite-time isothermal process.

quant-ph↗

arXiv2021

Optimizing Thermodynamic Cycles with Two Finite-Sized Reservoirs

We study the non-equilibrium thermodynamics of a heat engine operating between two finite-sized reservoirs with well-defined temperatures. Within the linear response regime, it is found that the uniform temperature of the two reservoirs at final time $τ$ is bounded from below by the entropy production $σ_{\mathrm{min}}\propto1/τ$. We discover a general power-efficiency trade-off depending on the ratio of heat capacities ($γ$) of the reservoirs for the engine. And a universal efficiency at maximum average power of the engine for arbitrary $γ$ is obtained. For practical purposes, the operation protocol of an ideal gas heat engine to achieve the optimal performance associated with $σ_{\mathrm{min}}$ is demonstrated. Our findings can be used to develop an general optimization scenario for thermodynamic cycles with finite-sized reservoirs in real-world circumstances.

cond-mat.stat-mech↗

arXiv2021

Works with quantum resource of coherence

We study the modification of the second law of thermodynamics for a quantum system interacting with a reservoir regarding quantum coherence. The whole system is isolated so that neither energy nor information is lost. It is discovered that the coherence of the reservoir can serves as a useful resource allowing the system extract more energy from the reservoir; among the coherence measures, only is the relative entropy of coherence feasible to quantitatively characterize energy exchange. We demonstrate that a thermodynamic cycle between two coherent reservoirs can output more work than its classical counterpart. The efficiency of such cycle surpasses the Carnot efficiency, which is the upper bound of heat engine efficiency in classical regime.

quant-ph↗

arXiv2021

Efficiency statistics of a quantum Otto cycle

The stochastic efficiency [G. Verley et al., Nat. Commun. 5, 4721 (2014)] was introduced to evaluate the performance of energy-conversion machines in micro-scale. However, such an efficiency generally diverges when no heat is absorbed while work is produced in a thermodynamic cycle. As a result, any statistical moments of the efficiency do not exist. In this study, we come up with a different version of the definition for the stochastic efficiency which is always finite. Its mean value is equal to the conventional efficiency, and higher moments characterize the fluctuations of the cycle. In addition, the fluctuation theorems are re-expressed via the efficiency. For working substance satisfying the equipartition theorem, we clarify that the thermodynamic uncertainty relation for efficiency is valid in an Otto engine. To demonstrate our general discussions, the efficiency statistics of a quantum harmonic-oscillator Otto engine is systematically investigated. The probability that the stochastic efficiency surpasses the Carnot efficiency is explicitly obtained. This work may shed new insight for optimizing micro-machines with fluctuations.

cond-mat.stat-mech↗

arXiv2020

The uniqueness of the integration factor associated with the exchanged heat in thermodynamics

State functions play important roles in thermodynamics. Different from the process function, such as the exchanged heat $δQ$ and the applied work $δW$, the change of the state function can be expressed as an exact differential. We prove here that, for a generic thermodynamic system, only the inverse of the temperature, namely $1/T$, can serve as the integration factor for the exchanged heat $δQ$. The uniqueness of the integration factor invalidates any attempt to define other state functions associated with the exchanged heat, and in turn, reveals the incorrectness of defining the entransy $E_{vh}=C_VT^2 /2$ as a state function by treating $T$ as an integration factor. We further show the errors in the derivation of entransy by treating the heat capacity $C_V$ as a temperature-independent constant.

cond-mat.stat-mech↗

arXiv2020

Self-consistency of optimizing finite-time Carnot engines with the low-dissipation model

The efficiency at the maximum power (EMP) for finite-time Carnot engines established with the low-dissipation model, relies significantly on the assumption of the inverse proportion scaling of the irreversible entropy generation $ΔS^{(\mathrm{ir})}$ on the operation time $τ$, i.e., $ΔS^{(\mathrm{ir})}\propto1/τ$. The optimal operation time of the finite-time isothermal process for EMP has to be within the valid regime of the inverse proportion scaling. Yet, such consistency was not tested due to the unknown coefficient of the $1/τ$-scaling. In this paper, using a two-level atomic heat engine as an illustration, we reveal that the optimization of the finite-time Carnot engines with the low-dissipation model is self-consistent only in the regime of $η_{\mathrm{C}}\ll1$, where $η_{\mathrm{C}}$ is the Carnot efficiency. In the large-$η_{\mathrm{C}}$ regime, the operation time for EMP obtained with the low-dissipation model is not within the valid regime of the $1/τ$-scaling, and the exact EMP is found to surpass the well-known bound $η_{+}=η_{\mathrm{C}}/(2-η_{\mathrm{C}})$

quant-ph↗

arXiv2019

Experimental validation of the $1/τ$ -scaling entropy generation in finite-time thermodynamics with dry air

The second law of thermodynamics can be described as the non-decreasing of the entropy in the irreversible thermodynamic process. Such phenomenon can be quantitatively evaluated with the irreversible entropy generation (IEG), which was recently found to follow a $1/τ$ scaling for the system under a long contact time $τ$ with the thermal bath. This scaling, predicted in many finite-time thermodynamic models, is of great potential in the optimization of heat engines, yet remains lack of direct experimental validation. In this letter, we design an experimental apparatus to test such scaling by compressing dry air in a temperature-controlled water bath. More importantly, we quantitatively verify the optimized control protocol to reduce the IEG. Such optimization shall bring new insight to the practical design of heat engine cycles.

cond-mat.stat-mech↗

arXiv2019

Effect of finite-size heat source's heat capacity on the efficiency of heat engine

Heat engines used to output useful work have important practical significance, which, in general, operate between heat baths of infinite size and constant temperature. In this paper we study the efficiency of a heat engine operating between two finite-size heat sources with initial temperature differences. The total output work of such heat engine is limited due to the finite heat capacity of the sources. We investigate the effects of different heat capacity characteristics of the sources on the heat engine's efficiency at maximum work (EMW) in the quasi-static limit. In addition, we study the efficiency of the engine working in finite-time with maximum power of each cycle is achieved and find the efficiency follows a simple universality as $η=η_{\mathrm{C}}/4+O\left(η_{\mathrm{C}}^{2}\right)$. Remarkably, when the heat capacity of the heat source is negative, such as the black holes, we show that the heat engine efficiency during the operation can surpass the Carnot efficiency determined by the initial temperature of the heat sources. It is further argued that the heat engine between two black holes with vanishing initial temperature difference can be driven by the energy fluctuation. The corresponding EMW is proved to be $η_{\mathrm{EMW}}=2-\sqrt{2}$, which is two time of the maximum energy release rate $μ=\left(2-\sqrt{2}\right)/2\approx0.29$ of two black hole emerging process obtained by S. W. Hawking.

cond-mat.stat-mech↗

arXiv2019

Directional quantum random walk induced by coherence

Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation between different steps in QW and leads to a ballistic position distribution. In this paper, we propose an alternative quantum extension of CRW from the ensemble interpretation, named quantum random walk (QRW), where the walker has many unrelated coins, modeled as two-level systems, initially prepared in the same state. We calculate the walker's position distribution in QRW for different initial coin states with the coin operator chosen as Hadamard matrix. In one-dimensional case, the walker's position is the asymmetric binomial distribution. We further demonstrate that in QRW, coherence leads the walker to perform directional movement. For an initially decoherenced coin state, the walker's position distribution is exactly the same as that of CRW. Moreover, we study QRW in 2D lattice, where the coherence plays a more diversified role in the walker's position distribution.

quant-ph↗

arXiv2018

Universal constraint for efficiency and power of a low-dissipation heat engine

The constraint relation for efficiency and power is crucial to design optimal heat engines operating within finite time. We find a universal constraint between efficiency and output power for heat engines operating in the low-dissipation regime. Such constraint is validated with an example of Carnot-like engine. Its microscopic dynamics is governed by the master equation. Based on the master equation, we connect the microscopic coupling strengths to the generic parameters in the phenomenological model. We find the usual assumption of low-dissipation is achieved when the coupling to thermal environments is stronger than the driving speed. Additionally, such connection allows the design of practical cycle to optimize the engine performance.

quant-ph↗

arXiv2018

Optimal operating protocol to achieve efficiency at maximum power of heat engines

The efficiency at maximum power has been investigated extensively, yet the practical control scheme to achieve it remains elusive. We fill such gap with a stepwise Carnot-like cycle, which consists the discrete isothermal process (DIP) and adiabatic process. With DIP, we validate the widely adopted assumption of \mathscr{C}/t relation of the irreversible entropy generation S^{(\mathrm{ir})}, and show the explicit dependence of the coefficient \mathscr{C} on the fluctuation of the speed of tuning energy levels as well as the microscopic coupling constants to the heat baths. Such dependence allows to control the irreversible entropy generation by choosing specific control schemes. We further demonstrate the achievable efficiency at maximum power and the corresponding control scheme with the simple two-level system. Our current work opens new avenues for the experimental test, which was not feasible due to the lack the of the practical control scheme in the previous low-dissipation model or its equivalents.

quant-ph↗

arXiv2018

Non-thermal radiation of black hole off canonical typicality

We study the Hawking radiation of black holes by considering the canonical typicality. For the universe consisting of black holes and their outer part, we directly obtain a non-thermal radiation spectrum of an arbitrary black hole from its entropy, which only depends on a few external qualities (known as hairs), such as mass, charge, and angular momentum. Our result shows that the spectrum of the non-thermal radiation is independent of the detailed quantum tunneling dynamics across black hole horizon. We prove that the black hole information paradox is naturally resolved by taking account the correlation between black hole and its radiation in our approach.

quant-ph↗