Fluctuation theorem for entropy production at strong coupling

Fluctuation theorems have been applied successfully to any system away from thermal equilibrium, which are helpful for understanding the thermodynamic state evolution. We investigate fluctuation theorems for strong coupling between a system and its reservoir, by path-dependent definition of work and heat satisfying the first law of thermodynamics. We present the fluctuation theorems for two kinds of entropy productions. One is the informational entropy production, which is always non-negative and can be employed in either strong or weak coupling systems. The other is the thermodynamic entropy production, which differs from the informational entropy production at strong coupling by the effects regarding the reservoir. We find that, it is the negative work on the reservoir, rather than the nonequilibrium of the thermal reservoir,which invalidates the thermodynamic entropy production at strong coupling. Our results indicate that the effects from the reservoir are essential to understanding thermodynamic processes at strong coupling.     

Fluctuation theorem and chaos

The heat theorem (i.e. the second law of thermodynamics or the existence of entropy) is a manifestation of a general property of hamiltonian mechanics and of the ergodic hypothesis. In nonequilibrium thermodynamics of stationary states the chaotic hypothesis plays a similar role: it allows a unique determination of the probability distribution (called SRB distribution) on phase space providing the time averages of the observables. It also implies an expression for a few averages concrete enough to derive consequences of symmetry properties like the fluctuation theorem or to formulate a theory of coarse graining unifying the foundations of equilibrium and of nonequilibrium.     

Fluctuation theorem for stochastic systems

The fluctuation theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics. It has been proved in a number of different ways for thermostatted deterministic nonequilibrium systems. In the present paper we show that the fluctuation theorem is also valid for a class of stochastic nonequilibrium systems. The theorem is therefore not reliant on the reversibility or the determinism of the underlying dynamics. Numerical tests verify the theoretical result.     

Fluctuation theorem in quantum heat conduction

We consider steady-state heat conduction across a quantum harmonic chain connected to reservoirs modeled by infinite collection of oscillators. The heat, Q, flowing across the oscillator in a time interval tau is a stochastic variable and we study the probability distribution function P(Q). We compute the exact generating function of Q at large tau and the large deviation function. The generating function has a symmetry satisfying the steady-state fluctuation theorem without any quantum corrections. The distribution P(Q) is non-Gaussian with clear exponential tails. The effect of finite tau and nonlinearity is considered in the classical limit through Langevin simulations. We also obtain the prediction of quantum heat current fluctuations at low temperatures in clean wires.     

Non-equilibrium thermodynamic potential and flux fluctuation theorem

A flux fluctuation theorem proposed recently [Seitaridou, et al., J. Phys. Chem. B 111 (2007) 2288] on the relative probability of direct and reverse diffusion fluxes in a non-equilibrium steady state is related here to a non-equilibrium thermodynamic potential used in extended irreversible thermodynamics. This connection allows one to provide a new derivation of the theorem, which complements the previous one, to generalize it to other fluxes, and illustrates the thermodynamic relevance of this theorem.     

Interrelation between the integral Lagrangian and thermodynamic entropy

The states of a crystalline body near absolute zero are studied in terms of mechanics and thermodynamics. A formal correlation between the integral Lagrangian of the “mechanical“ origin and thermodynamic entropy is established.     

Nonequilibrium expressions for entropy and other thermodynamic quantities

The entropy is written as a density series expansion involving a new kind of cumulant. These are defined as usual from the so-called reduced distribution functions. The first four terms of the series expansion of the entropy are shown to be identical to the known result. When density corrections are retained up to theuth order, the entropy is proved to obey approximately a conservation theorem. Finally, a discussion of nonequilibrium and equilibrium properties of the grand canonical ensemble is presented.     

Microscopic diagonal entropy and its connection to basic thermodynamic relations

We define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as S_d=-∑_nρ_nnlnρ_nn with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the conventional von Neumann entropy S_n = −Trρ ln ρ. However, in contrast to S_n, the d-entropy is not conserved in time in closed Hamiltonian systems. If the system is initially in stationary state then in accord with the second law of thermodynamics the d-entropy can only increase or stay the same. We also show that the d-entropy can be expressed through the energy distribution function and thus it is measurable, at least in principle. Under very generic assumptions of the locality of the Hamiltonian and non-integrability the d-entropy becomes a unique function of the average energy in large systems and automatically satisfies the fundamental thermodynamic relation. This relation reduces to the first law of thermodynamics for quasi-static processes. The d-entropy is also automatically conserved for adiabatic processes. We illustrate our results with explicit examples and show that S_d behaves consistently with expectations from thermodynamics.     

Fluctuation theorem for currents in the Spinning Lorentz Gas

We study the fluctuation theorem formulated in terms of the currents present in a Hamiltonian system with coupled mass and energy transport. To drive the system out of equilibrium, we assume it to be connected to two ideal thermodynamical baths. The fluctuation symmetry is, thus, expressed in terms of the joint probability distribution of energy and particle currents in the system. This relation is verified numerically for the stationary state in the Spinning Lorentz Gas (SLG), driven out of equilibrium by temperature and/or chemical potential differences between the baths, as well as in the presence of an applied field.     

Applicability of minimum entropy generation methodto optimizing thermodynamic cycles

Entropy generation is often used as a figure of merit in thermodynamic cycle optimizations. In this paper, it is shown that the applicability of the minimum entropy generation method to optimizing output power is conditional. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power when the total heat into the system of interest is not prescribed. For the cycles whose working medium is heated or cooled by streams with prescribed inlet temperatures and prescribed heat capacity flow rates, it is theoretically proved that both the minimum entropy generation rate and the minimum entropy generation number correspond to the maximum output power when the virtual entropy generation induced by dumping the used streams into the environment is considered. However, the minimum principle of entropy generation is not tenable in the case that the virtual entropy generation is not included, because the total heat into the system of interest is not fixed. An irreversible Carnot cycle and an irreversible Brayton cycle are analysed. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power if the heat into the system of interest is not prescribed.     

太阳能喷射式制冷循环的热力学熵分析

利用熵分析法对太阳能喷射式制冷循环进行分析。找出系统中不可逆损失在各环节中的分布情况,分析其原因。并且研究发生温度、蒸发温度等系统参数对循环的影响,还分析了工况的变化对循环性能的影响。     

Sen黑洞熵与能斯特定理

避开求解黑洞背景下波动方程的困难,应用量子统计方法,直接求解轴对称Sen黑洞背景下Bose场和Fermi场的配分函数.然后利用改进的 brick-wall 方法-膜模型,计算黑洞背景下Bose场和Fermi场的熵.得到黑洞熵不但与黑洞的外视界面积有关，而且也是内视界面积的函数.在所得结论中不存在对数发散项与舍去项,也不存在黑洞视界外标量场或Dirac场为什么是黑洞熵疑难,并且给出粒子的自旋简并度对黑洞熵的影响. 当黑洞的辐射温度趋于绝对零度时,由黑洞内外视界面积决定的黑洞熵也趋于零,它满足能斯特定理,可视 关键词： 膜模型 黑洞熵 能斯特定理     

An application of a representation theorem for entropy functionals

The vibrational predissociation of HD₂ ⁺ is modelled in terms of quantum-mechanical tunnelling through a minimal centrifugal barrier at given total angular momentum, J, and with statistical intermode coupling behind the barrier. It is shown that the observed strong preference for the H⁺ + D ₂ predissociation channel (over D⁺ + HD) is consistent with an experimental preference for J values in the range 0 < J < 25, a range which is also shown to be consistent with the observed H₃ ⁺ preferred range of kinetic energy release. A correlation between the total angular momentum and the kinetic energy release is also predicted.     

Applicability of the minimum entropy generation method for optimizing thermodynamic cycles

Entropy generation is often used as a figure of merit in thermodynamic cycle optimizations. In this paper, it is shown that the applicability of the minimum entropy generation method to optimizing output power is conditional. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power when the total heat into the system of interest is not prescribed. For the cycles whose working medium is heated or cooled by streams with prescribed inlet temperatures and prescribed heat capacity flow rates, it is theoretically proved that both the minimum entropy generation rate and the minimum entropy generation number correspond to the maximum output power when the virtual entropy generation induced by dumping the used streams into the environment is considered. However, the minimum principle of entropy generation is not tenable in the case that the virtual entropy generation is not included, because the total heat into the system of interest is not fixed. An irreversible Carnot cycle and an irreversible Brayton cycle are analysed. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power if the heat into the system of interest is not prescribed.     

单势阱粒子溢流模型中热力学量的涨落效应

采用相空间积分方法严格导出了各态历经条件下单势阱粒子溢流模型中系统温度和阱内粒子数涨落的解析表达式,着重讨论了热力学量涨落与总粒子数和势阱体积之间的关系.研究表明,系统总粒子数越少以及势阱体积越小,热力学涨落越显著,并且热力学涨落与阱内粒子的溢出密切相关.粒子的溢出和系统负比热及热力学大幅涨落的发生存在一一对应的关系,这一对应关系的根源可以从表观能量逆均分来理解.     

Fluctuation theorem for the mutation process in in vitro evolution

A proposition based on the fluctuation theorem in thermodynamics is formulated to quantitatively describe molecular evolution processes in biology.Although we cannot give full proof of its generality,we demonstrate via computer simulation its applicability in an example of DNA in vitro evolution.According to this theorem,the evolution process is a series of exponentially rare fluctuations fixed by the force of natural selection.     

A thermodynamic basis for the electronic properties of molten semiconductors: the role of electronic entropy

Abstract

The thermodynamic origin of a relation between features of the phase diagrams and the electronic properties of molten semiconductors is provided. Leveraging a quantitative connection between electronic properties and entropy, a criterion is derived to establish whether a system will retain its semiconducting properties in the molten phase. It is shown that electronic entropy is critical to the thermodynamics of molten semiconductor systems, driving key features of phase diagrams including, for example, miscibility gaps.