arXiv subjects

Z. C. Tu

Publications and source records attributed to Z. C. Tu.

At least 37 records · Page 2Linked to original sources

arXiv2019

Stochastic thermodynamics with odd controlling parameters

Stochastic thermodynamics extends the notions and relations of classical thermodynamics to small systems that experience strong fluctuations. The definitions of work and heat and the microscopically reversible condition are two key concepts in the current framework of stochastic thermodynamics. Herein, we apply stochastic thermodynamics to small systems with odd controlling parameters and find that the definition of heat and the microscopically reversible condition are incompatible. Such a contradiction also leads to a revision to the fluctuation theorems and nonequilibrium work relations. By introducing adjoint dynamics, we find that the total entropy production can be separated into three parts, with two of them satisfying the integral fluctuation theorem. Revising the definitions of work and heat and the microscopically reversible condition allows us to derive two sets of modified nonequilibrium work relations, including the Jarzynski equality, the detailed Crooks work relation, and the integral Crooks work relation. We consider the strategy of shortcuts to isothermality as an example and give a more sophisticated explanation for the Jarzynski-like equality derived from shortcuts to isothermality.

cond-mat.stat-mech↗

arXiv2017

Shortcuts to isothermality and nonequilibrium work relations

In conventional thermodynamics, it is widely acknowledged that the realization of an isothermal process for a system requires a quasi-static controlling protocol. Here we propose and design a strategy to realize a finite-rate isothermal transition from an equilibrium state to another one with same temperature, which is named shortcut to isothermality~(STI). By using STI, we unexpectedly derive three nonequilibrium work relations, including an identity between the free energy difference and the mean work due to the potential of the original system, a generalized Jarzynski equality, and the inverse relationship between the irreversible work and the total driving time. We numerically confirm these three relations by considering the motion of a Brownian particle trapped in a harmonic potential and dragged by a time-dependent force.

cond-mat.stat-mech↗

arXiv2017

General neck condition for the limit shape of budding vesicles

The shape equation and linking conditions for a vesicle with two-phase domains are derived. We refine the conjecture on the general neck condition for the limit shape of a budding vesicle proposed by Jülicher and Lipowsky [Phys. Rev. Lett. \textbf{70}, 2964 (1993); Phys. Rev. E \textbf{53}, 2670 (1996)], and then we use the shape equation and linking conditions to prove that this conjecture holds not only for axisymmetric budding vesicles, but also for asymmetric ones. Our study reveals that the mean curvature at any point on the membrane segments adjacent to the neck satisfies the general neck condition for the limit shape of a budding vesicle when the length scale of the membrane segments is much larger than the characteristic size of the neck but still much smaller than the characteristic size of the vesicle.

cond-mat.soft↗

arXiv2016

First integrals of the axisymmetric shape equation of lipid membranes

The shape equation of lipid membranes [Zhong-can and Helfrich(1987) PRL 59 2486] is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu [Zheng and Liu(1993) PRE 48 2856]. Here we try to further reduce this second-order ODE to a first-order ODE by seeking for first integrals according to the Noether theorem. We indeed find a first integral when the second-order ODE is invariant under conformation transformations. We obtain the mechanical interpretation of the first integral by using the membrane stress tensor.

math-ph↗

arXiv2015

Retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential

The retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential is investigated in the overdamped and underdamped situations, respectively. Because of different time scales, the overdamped and underdamped Langevin equations (as well as the corresponding Fokker-Planck equations) lead to distinctive restrictions on protocols maintaining canonical distributions. Two special cases are analyzed in details: First, a Brownian particle is controlled by a time-dependent harmonic potential and embedded in medium with constant temperature; Second, a Brownian particle is controlled by a time-dependent harmonic potential and embedded in a medium whose temperature is tuned together with the potential stiffness to keep a constant effective temperature of the Brownian particle. We find that the canonical distributions are usually retainable for both the overdamped and underdamped situations in the former case. However, the canonical distributions are retainable merely for the overdamped situation in the latter case. We also investigate general time-dependent potentials beyond the harmonic form and find that the retainability of canonical distributions depends sensitively on the specific form of potentials.

cond-mat.stat-mech↗

arXiv2015

Hidden symmetries and nonlinear constitutive relations for tight-coupling heat engines

Typical heat engines exhibit a kind of homotypy: The heat exchanges between a cyclic heat engine and its two heat reservoirs abide by the same function type; the forward and backward flows of an autonomous heat engine also conform to the same function type. This homotypy mathematically reflects in the existence of hidden symmetries for heat engines. The heat exchanges between the cyclic heat engine and its two reservoirs are dual under the joint transformation of parity inversion and time-reversal operation. Similarly, the forward and backward flows in the autonomous heat engine are also dual under the parity inversion. With the consideration of these hidden symmetries, we derive a generic nonlinear constitutive relation up to the quadratic order for tight-coupling cyclic heat engines and that for tight-coupling autonomous heat engines, respectively.

cond-mat.stat-mech↗

arXiv2015

Constitutive Relation for Nonlinear Response and Universality of Efficiency at Maximum Power for Tight-Coupling Heat Engines

We present a unified perspective on nonequilibrium heat engines by generalizing nonlinear irreversible thermodynamics. For tight-coupling heat engines, a generic constitutive relation of nonlinear response accurate up to the quadratic order is derived from the symmetry argument and the stall condition. By applying this generic nonlinear constitutive relation to finite-time thermodynamics, we obtain the necessary and sufficient condition for the universality of efficiency at maximum power, which states that a tight-coupling heat engine takes the universal efficiency at maximum power up to the quadratic order if and only if either the engine symmetrically interacts with two heat reservoirs or the elementary thermal energy flowing through the engine matches the characteristic energy of the engine. As a result, we solve the following paradox: On the one hand, the universal quadratic term in the efficiency at maximum power for tight-coupling heat engines proved as a consequence of symmetry [M. Esposito, K. Lindenberg, and C. Van den Broeck, Phys. Rev. Lett. 102, 130602 (2009); S. Q. Sheng and Z. C. Tu, Phys. Rev. E 89, 012129 (2014)]; On the other hand, two typical heat engines including the Curzon-Ahlborn endoreversible heat engine [F. L. Curzon and B. Ahlborn, Am. J. Phys. 43, 22 (1975)] and the Feynman ratchet [Z. C. Tu, J. Phys. A 41, 312003 (2008)] recover the universal efficiency at maximum power regardless of any symmetry.

cond-mat.stat-mech↗

arXiv2014

Stochastic heat engine with the consideration of inertial effects and shortcuts to adiabaticity

When a Brownian particle in contact with a heat bath at a constant temperature is controlled by a time-dependent harmonic potential, its distribution function can be rigorously derived from the Kramers equation with the consideration of the inertial effect of the Brownian particle. Based on this rigorous solution and the concept of shortcuts to adiabaticity, we construct a stochastic heat engine by employing the time-dependent harmonic potential to manipulate the Brownian particle to complete a thermodynamic cycle. We find that the efficiency at maximum power of this stochastic heat engine is equal to $1-\sqrt{T_c/T_h}$ where $T_c$ and $T_h$ are the temperatures of the cold bath and the hot one in the thermodynamic cycle, respectively.

cond-mat.stat-mech↗

arXiv2014

Recent theoretical advances in elasticity of membranes following Helfrich's spontaneous curvature model

Recent theoretical advances in elasticity of membranes following Helfrich's famous spontaneous curvature model are summarized in this review. The governing equations describing equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are presented. Several analytic solutions to these equations and their corresponding configurations are demonstrated.

cond-mat.soft↗

arXiv2014

Coefficient of performance at maximum χ-criterion for Feynman ratchet as a refrigerator

The χ-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per-unit-time by the working substance [de Tomás et al., Phys. Rev. E, 85 (2012) 010104(R)]. The χ-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum χ-criterion for Feynman ratchet are investigated at both large and small temperature difference. An interpolation formula, which fits the numerical solution very well, is proposed. Besides, the sufficient condition for the universality of the coefficient of performance at maximum χis investigated.

cond-mat.stat-mech↗

arXiv2014

Weighted reciprocal of temperature, weighted thermal flux, and their applications in finite-time thermodynamics

The concepts of weighted reciprocal of temperature and weighted thermal flux are proposed for a heat engine operating between two heat baths and outputting mechanical work. With the aid of these two concepts, the generalized thermodynamic fluxes and forces can be expressed in a consistent way within the framework of irreversible thermodynamics. Then the efficiency at maximum power output for a heat engine, one of key topics in finite-time thermodynamics, is investigated on the basis of a generic model under the tight-coupling condition. The corresponding results have the same forms as those of low-dissipation heat engines [M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, {Phys. Rev. Lett.} \textbf{105}, 150603 (2010)]. The mappings from two kinds of typical heat engines, such as the low-dissipation heat engine and the Feynman ratchet, into the present generic model are constructed. The universal efficiency at maximum power output up to the quadratic order is found to be valid for a heat engine coupled symmetrically and tightly with two baths. The concepts of weighted reciprocal of temperature and weighted thermal flux are also transplanted to the optimization of refrigerators.

cond-mat.stat-mech↗

arXiv2013

Universality of energy conversion efficiency for optimal tight-coupling heat engines and refrigerators

A unified $χ$-criterion for heat devices (including heat engines and refrigerators) which is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tomás \emph{et al} 2012 \textit{Phys. Rev. E} \textbf{85} 010104(R)] is optimized for tight-coupling heat engines and refrigerators operating between two heat baths at temperatures $T_c$ and $T_h(>T_c)$. By taking a new convention on the thermodynamic flux related to the heat transfer between two baths, we find that for a refrigerator tightly and symmetrically coupled with two heat baths, the coefficient of performance (i.e., the energy conversion efficiency of refrigerators) at maximum $χ$ asymptotically approaches to $\sqrt{\varepsilon_C}$ when the relative temperature difference between two heat baths $\varepsilon_C^{-1}\equiv (T_h-T_c)/T_c$ is sufficiently small. Correspondingly, the efficiency at maximum $χ$ (equivalent to maximum power) for a heat engine tightly and symmetrically coupled with two heat baths is proved to be $η_C/2+η_C^2/8$ up to the second order term of $η_C\equiv (T_h-T_c)/T_h$, which reverts to the universal efficiency at maximum power for tight-coupling heat engines operating between two heat baths at small temperature difference in the presence of left-right symmetry [Esposito \emph{et al} 2009 \textit{Phys. Rev. Lett.} \textbf{102} 130602].

cond-mat.stat-mech↗

arXiv2013

Bounds and phase diagram of efficiency at maximum power for tight-coupling molecular motors

The efficiency at maximum power (EMP) for tight-coupling molecular motors is investigated within the framework of irreversible thermodynamics. It is found that the EMP depends merely on the constitutive relation between the thermodynamic current and force. The motors are classified into four generic types (linear, superlinear, sublinear, and mixed types) according to the characteristics of the constitutive relation, and then the corresponding ranges of the EMP for these four types of molecular motors are obtained. The exact bounds of the EMP are derived and expressed as the explicit functions of the free energy released by the fuel in each motor step. A phase diagram is constructed which clearly shows how the region where the parameters (the load distribution factor and the free energy released by the fuel in each motor step) are located can determine whether the value of the EMP is larger or smaller than 1/2. This phase diagram reveals that motors using ATP as fuel under physiological conditions can work at maximum power with higher efficiency ($>1/2$) for a small load distribution factor ($<0.1$).

cond-mat.stat-mech↗

arXiv2013

Bounds of Efficiency at Maximum Power for Normal-, Sub- and Super-Dissipative Carnot-Like Heat Engines

The Carnot-like heat engines are classified into three types (normal-, sub- and super-dissipative) according to relations between the minimum irreversible entropy production in the "isothermal" processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between $η_C/2$ and $η_C/(2-η_C)$, $η_C /2$ and $η_C$, 0 and $η_C/(2-η_C)$, respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Lett. 98, 40001 (2012)] although the dissipative engines and the irreversible ones are inequivalent to each other.

cond-mat.stat-mech↗

arXiv2013

Challenges in theoretical investigations on configurations of lipid membranes

This review reports some key results in theoretical investigations on configurations of lipid membranes and presents several challenges in this field which involve (i) exact solutions to the shape equation of lipid vesicles; (ii) exact solutions to the governing equations of open lipid membranes; (iii) neck condition of two-phase vesicles in the budding state; (iv) nonlocal theory of membrane elasticity; (v) relationship between symmetry and the magnitude of free energy.

cond-mat.soft↗

arXiv2012

Coefficient of performance at maximum figure of merit and its bounds for low-dissipation Carnot-like refrigerators

The figure of merit for refrigerators performing finite-time Carnot-like cycles between two reservoirs at temperature $T_h$ and $T_c$ ($<T_h$) is optimized. It is found that the coefficient of performance at maximum figure of merit is bounded between 0 and $(\sqrt{9+8\varepsilon_c}-3)/2$ for the low-dissipation refrigerators, where $\varepsilon_c =T_c/(T_h-T_c)$ is the Carnot coefficient of performance for reversible refrigerators. These bounds can be reached for extremely asymmetric low-dissipation cases when the ratio between the dissipation constants of the processes in contact with the cold and hot reservoirs approaches to zero or infinity, respectively. The observed coefficients of performance for real refrigerators are located in the region between the lower and upper bounds, which is in good agreement with our theoretical estimation.

cond-mat.stat-mech↗

arXiv2012

Bounds of efficiency at maximum power for linear, superlinear and sublinear irreversible Carnot-like heat engines

The efficiency at maximum power (EMP) of irreversible Carnot-like heat engines is investigated based on the weak endoreversible assumption and the phenomenologically irreversible thermodynamics. It is found that the weak endoreversible assumption can reduce to the conventional one for the heat engines working at maximum power. Carnot-like heat engines are classified into three types (linear, superlinear, and sublinear) according to different characteristics of constitutive relations between the heat transfer rate and the thermodynamic force. The EMPs of Carnot-like heat engines are proved to be bounded between $η_C/2$ and $η_C/(2-η_C)$ for the linear type, 0 and $η_C/(2-η_C)$ for the superlinear type, and $η_C/2$ and $η_C$ for the sublinear type, respectively, where $η_C$ is the Carnot efficiency.

cond-mat.stat-mech↗

arXiv2011

Efficiency at maximum power output of linear irreversible Carnot-like heat engines

The efficiency at maximum power output of linear irreversible Carnot-like heat engines is investigated based on the assumption that the rate of irreversible entropy production of working substance in each "isothermal" process is a quadratic form of heat exchange rate between the working substance and the reservoir. It is found that the maximum power output corresponds to minimizing the irreversible entropy production in two "isothermal" processes of the Carnot-like cycle, and that the efficiency at maximum power output has the form as $η_{mP}={η_C}/(2-γη_C)$ where $η_C$ is the Carnot efficiency while $γ$ depends on the heat transfer coefficients between the working substance and two reservoirs. The value of $η_{mP}$ is bounded between $η_{-}\equiv η_C/2$ and $η_{+}\equivη_C/(2-η_C)$. These results are consistent with those obtained by Chen and Yan [J. Chem. Phys. \textbf{90}, 3740 (1989)] based on the endoreversible assumption, those obtained by Esposito \textit{et al.} [Phys. Rev. Lett. \textbf{105}, 150603 (2010)] based on the low-dissipation assumption, and those obtained by Schmiedl and Seifert [EPL \textbf{81}, 20003 (2008)] for stochastic heat engines which in fact also satisfy the low-dissipation assumption. Additionally, we find that the endoreversible assumption happens to hold for Carnot-like heat engines operating at the maximum power output based on our fundamental assumption, and that the Carnot-like heat engines that we focused does not strictly satisfy the low-dissipation assumption, which implies that the low-dissipation assumption or our fundamental assumption is a sufficient but non-necessary condition for the validity of $η_{mP}={η_C}/(2-γη_C)$ as well as the existence of two bounds $η_{-}\equiv η_C/2$ and $η_{+}\equivη_C/(2-η_C)$.

cond-mat.stat-mech↗