Variational principles and thermodynamics

随机热力学的变分公式：有限维系统

Variational formulation of stochastic thermodynamics: Finite-dimensional systems

本文提出随机热力学的变分基础，通过第二定律推导出一致的热力学结构，推导出新的广义涨落耗散关系，并在扩展热力学相空间中扩展了随机热力学的关键结果。

随机热力学的变分形式：空间扩展系统

A variational formulation of stochastic thermodynamics: Spatially extended systems

本文提出一种变分形式，用于构建热力学一致的随机场理论，通过扩展经典场论的哈密顿原理，引入第二定律作为公理，推导出新的涨落耗散关系，并在扩展相空间中保持与标准随机热力学一致的熵产形式。

Quantization of Thermodynamics, Supersecondary Quantization, and a New Variational Principle

In solving the problem of finding a temperature distribution which, at zero temperature, corresponds to superfluidity, i.e., to nonzero energy, the author tried to quantize free energy. This was done on the basis of supersecondary quantization whose special case is the usual secondary quantization for bosons and with the help of which new representations of the Schrödinger equation were obtained. The supersecondary quantization allowed the author to construct a variational method whose zero approximation are the Hartree-Fock and Bogolyubov-BCSch variational principles. This method works especi…

Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density-functional formulation, and nature of steady-state forces

The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum-statistical mechanics provide consistent but computational costly approaches; alternatively, use of density-dependent ballistic-transport calculations [e.g., Phys. Rev. B 52, 5335 (1995)], here denoted `DBT', provide computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory fo…

Conservation-Dissipation Formalism for Soft Matter Physics: I. Equivalence with Doi's Variational Approach

In this paper, we proved that by choosing the proper variational function and variables, the variational approach proposed by M. Doi in soft matter physics was equivalent to the Conservation-Dissipation Formalism. To illustrate the correspondence between these two theories, several novel examples in soft matter physics, including particle diffusion in dilute solutions, polymer phase separation dynamics and nematic liquid crystal flows, were carefully examined. Based on our work, a deep connection among the generalized Gibbs relation, the second law of thermodynamics and the variational princip…

汤川流体的变分方法。I. 热力学

Variational approach to Yukawa fluids. I. Thermodynamics

研究强耦合汤川流体，用变分方法以硬球流体为参考系统计算相关量，珀库斯-耶维克维里熵适用，与分子动力学模拟结果吻合好，可作预测工具，还估计了强屏蔽区熔化曲线位置。

Variational principle for fractional kinetics and the Lévy Ansatz

A variational principle is developed for fractional kinetics based on the auxiliary-field formalism. It is applied to the Fokker-Planck equation with spatio-temporal fractionality, and a variational solution is obtained with the help of the Lévy Ansatz. It is shown how the whole range from subdiffusion to superdiffusion is realized by the variational solution, as a competing effect between the long waiting time and the long jump. The motion of the center of the probability distribution is also analyzed in the case of a periodic drift.

Correlation functions from a unified variational principle: trial Lie groups

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest $\ldots$