Stochastic thermodynamics of chemical reaction networks

For chemical reaction networks described by a master equation, we define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction events. A first-law like energy balance relates internal energy, applied (chemical) work and dissipated heat for every single reaction. Entropy production along a single trajectory involves a sum over changes in the entropy of the network itself and the entropy of the medium. The latter is given by the exchanged heat identified through the first law. Total entropy production is constrained by an integral fluctuation theorem for networks arbitrarily driven by time-dependent rates and a detailed fluctuation theorem for networks in the steady state. Further exact relations like a generalized Jarzynski relation and a generalized Clausius inequality are discussed. We illustrate these results for a three-species cyclic reaction network which exhibits nonequilibrium steady states as well as transitions between different steady states.Comment: 14 pages, 2 figures, accepted for publication in J. Chem. Phy

Molecular kinetic analysis of a finite-time Carnot cycle

We study the efficiency at the maximal power $\eta_\mathrm{max}$ of a finite-time Carnot cycle of a weakly interacting gas which we can reagard as a nearly ideal gas. In several systems interacting with the hot and cold reservoirs of the temperatures $T_\mathrm{h}$ and $T_\mathrm{c}$, respectively, it is known that $\eta_\mathrm{max}=1-\sqrt{T_\mathrm{c}/T_\mathrm{h}}$ which is often called the Curzon-Ahlborn (CA) efficiency $\eta_\mathrm{CA}$. For the first time numerical experiments to verify the validity of $\eta_\mathrm{CA}$ are performed by means of molecular dynamics simulations and reveal that our $\eta_\mathrm{max}$ does not always agree with $\eta_\mathrm{CA}$, but approaches $\eta_\mathrm{CA}$ in the limit of $T_\mathrm{c} \to T_\mathrm{h}$. Our molecular kinetic analysis explains the above facts theoretically by using only elementary arithmetic.Comment: 6 pages, 4 figure

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 $\eta_C/2$ and $\eta_C/(2-\eta_C)$, $\eta_C /2$ and $\eta_C$, 0 and $\eta_C/(2-\eta_C)$, 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.Comment: 1 figur

Entropy and efficiency of a molecular motor model

In this paper we investigate the use of path-integral formalism and the concepts of entropy and traffic in the context of molecular motors. We show that together with time-reversal symmetry breaking arguments one can find bounds on efficiencies of such motors. To clarify this techinque we use it on one specific model to find both the thermodynamic and the Stokes efficiencies, although the arguments themselves are more general and can be used on a wide class of models. We also show that by considering the molecular motor as a ratchet, one can find additional bounds on the thermodynamic efficiency

Efficiency at maximum power: An analytically solvable model for stochastic heat engines

We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. For the efficiency at maximum power, we find a universal expression, different from the endoreversible Curzon-Ahlborn efficiency. Our results are illustrated with a simple one-dimensional engine working in and with a time-dependent harmonic potential.Comment: 6 pages, 3 figure

Thermoelectric efficiency at maximum power in a quantum dot

We identify the operational conditions for maximum power of a nanothermoelectric engine consisting of a single quantum level embedded between two leads at different temperatures and chemical potentials. The corresponding thermodynamic efficiency agrees with the Curzon-Ahlborn expression up to quadratic terms in the gradients, supporting the thesis of universality beyond linear response.Comment: 4 pages, 3 figure

Magnon-driven quantum-dot heat engine

We investigate a heat- to charge-current converter consisting of a single-level quantum dot coupled to two ferromagnetic metals and one ferromagnetic insulator held at different temperatures. We demonstrate that this nano engine can act as an optimal heat to spin-polarized charge current converter in an antiparallel geometry, while it acts as a heat to pure spin current converter in the parallel case. We discuss the maximal output power of the device and its efficiency.Comment: 6 pages, 4 figures, published version, selected as Editor's choic

Efficiency at maximum power of minimally nonlinear irreversible heat engines

We propose the minimally nonlinear irreversible heat engine as a new general theoretical model to study the efficiency at the maximum power $\eta^*$ of heat engines operating between the hot heat reservoir at the temperature $T_h$ and the cold one at $T_c$ ($T_c \le T_h$). Our model is based on the extended Onsager relations with a new nonlinear term meaning the power dissipation. In this model, we show that $\eta^*$ is bounded from the upper side by a function of the Carnot efficiency $\eta_C\equiv 1-T_c/T_h$ as $\eta^*\le \eta_C/(2-\eta_C)$. We demonstrate the validity of our theory by showing that the low-dissipation Carnot engine can easily be described by our theory.Comment: 6 pages, 1 figur

Efficiency of a Brownian information machine

A Brownian information machine extracts work from a heat bath through a feedback process that exploits the information acquired in a measurement. For the paradigmatic case of a particle trapped in a harmonic potential, we determine how power and efficiency for two variants of such a machine operating cyclically depend on the cycle time and the precision of the positional measurements. Controlling only the center of the trap leads to a machine that has zero efficiency at maximum power whereas additional optimal control of the stiffness of the trap leads to an efficiency bounded between 1/2, which holds for maximum power, and 1 reached even for finite cycle time in the limit of perfect measurements.Comment: 9 pages, 2 figure

Interaction of molecular motors can enhance their efficiency

Particles moving in oscillating potential with broken mirror symmetry are considered. We calculate their energetic efficiency, when acting as molecular motors carrying a load against external force. It is shown that interaction between particles enhances the efficiency in wide range of parameters. Possible consequences for artificial molecular motors are discussed.Comment: 6 pages, 8 figure