A general approach for deriving the expression of reference (density of) distribution functions, F^0, by statistical thermodynamics and the definition of local equilibrium conditions is illustrated. This procedure may be adopted for a system subject to an arbitrary number of thermodynamic forces. For concreteness, we analyze the case of a system submitted to three independent thermodynamic forces and the local equilibrium corresponds to the configuration of minimum entropy production condition and the maximum entropy principle. In this limit case, we show that the derived expression of distribution function is more general than that one, which is currently used for fitting the numerical steady-state solution obtained by simulating the Ion Cyclotron Radiation Heating (ICRH) FAST-plasmas and for describing various scenarios of tokamak plasmas. Through kinetic theory, we fixed the free parameters linking them with the external power supplies. The singularity at low energy in the proposed distribution function is related to the intermittency in the turbulent plasma. As a matter of fact, this work is not restricted to, but applied to, tokamak plasmas. Tokamak-plasmas are taken as an example of close thermodynamic systems. An application to a simple model of fully ionized tokamak-plasmas submitted to an external Ohmic source is discussed.
A Unified Nonequilibrium Framework: Thermodynamic Distance, Dissipation, and Stationary Laws via Effective State Count, Variational Stationarity, and Thermodynamic Bounds
Of dice and men. Subjective priors, gauge invariance, and nonequilibrium thermodynamics
勒内·马格利特（René Magritte）写道：“Ceci n 'est pas une pipe”，这只是烟斗的表现。现象和它们的物理描述是不同的，特别是支配前者的定律可能会享受对称性，而要达到后者就必须花费对称性。因此，惯性系是牛顿力学中的一个必要的数字，也是与实验相对抗的，但力学定律最终是独立于参考系的。推广了文献[M. Polettini，EPL 97（2012）30003]到连续系统，我们从基础的角度讨论了参考先验概率选择中的主观性如何成为热力学的（规范）对称性。特别地，先验的改变对应于坐标的改变。采用基于连续状态空间扩散过程的随机热力学的方法，我们讨论了熵和热力学观测值之间的差异，并表明，虽然熵的量化取决于先验，但热力学第二定律是用不变量，特别是热力学力的曲率来表示的（规范势），我们计算在几个例子中的过程导致不同的非平衡机制。
Thermodynamics Beyond Molecules: Statistical Thermodynamics of Distributions
统计热力学具有超越分子系统的普遍吸引力，然而，当它的工具被移植到物理学之外的领域时，基本问题\textit{what is thermodynamics?}仍然没有答案。我们在这里回答这个问题。广义统计热力学是概率分布的变分演算。它是独立的物理假设，但提供了一种手段，将我们的知识，假设和物理模型的随机过程，产生的概率问题。我们通过一个不涉及物理学的概率论证来推导熟悉的热力学演算。该理论的核心是一个分布空间和一个将概率分配给这个空间的特殊泛函。该泛函的最大化生成热力学关系的整个数学网络。我们得到统计力学作为一种特殊情况，并与信息论和贝叶斯推断。
