Unifying approach for fluctuation theorems from joint probability distributions

Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs

For driven open systems in contact with multiple heat reservoirs, we find the marginal distributions of work or heat do not satisfy any fluctuation theorem, but only the joint distribution of work and heat satisfies a family of fluctuation theorems. A hierarchical structure of these fluctuation theorems is discovered from microreversibility of the dynamics by adopting a step-by-step coarse-graining procedure in both classical and quantum regimes. Thus, we put all fluctuation theorems concerning work and heat into a unified framework. We also propose a general method to calculate the joint stat…

Thermodynamic inference in partially accessible Markov networks: A unifying perspective from transition-based waiting time distributions

The inference of thermodynamic quantities from the description of an only partially accessible physical system is a central challenge in stochastic thermodynamics. A common approach is coarse-graining, which maps the dynamics of such a system to a reduced effective one. While coarse-graining states of the system into compound ones is a well studied concept, recent evidence hints at a complementary description by considering observable transitions and waiting times. In this work, we consider waiting time distributions between two consecutive transitions of a partially observable Markov network.…

Joint fluctuation theorems for sequential heat exchange

We study the statistics of heat exchange of a quantum system that collides sequentially with an arbitrary number of ancillas. This can describe, for instance, an accelerated particle going through a bubble chamber. Unlike other approaches in the literature, our focus is on the \emph{joint} probability distribution that heat $Q_1$ is exchanged with ancilla 1, heat $Q_2$ is exchanged with ancilla 2, and so on. This allows one to address questions concerning the correlations between the collisional events. The joint distribution is found to satisfy a Fluctuation theorem of the Jarzynski-Wójcik ty…

Exact joint density-current probability function for the asymmetric exclusion process

We study the asymmetric exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach, and by the introduction of new operators satisfying a modified version of the original algebra.

Steady state statistics of driven diffusions

We consider overdamped diffusion processes driven out of thermal equilibrium and we analyze their dynamical steady fluctuations. We discuss the thermodynamic interpretation of the joint fluctuations of occupation times and currents; they incorporate respectively the time-symmetric and the time-antisymmetric sector of the fluctuations. We highlight the canonical structure of the joint fluctuations. The novel concept of traffic complements the entropy production for the study of the occupation statistics. We explain how the occupation and current fluctuations get mutually coupled out of equilibr…

第二类粒子的流涨落：联合统计

Current fluctuations for the second class particle : joint statistics

本文利用Bethe ansatz研究含单个第二类粒子的周期边界TASEP中两类粒子流的联合大偏差，发现其生成函数与开放边界TASEP的流涨落存在意外联系。

Statistical Mechanics of Entropy Production: Gibbsian hypothesis and local fluctuations

It is argued that a Gibbsian formula for the space-time distribution of microscopic trajectories of a nonequilibrium system provides a unifying framework for recent results on the fluctuations of the entropy production. The variable entropy production is naturally expressed as the time-reversal symmetry breaking part of the space-time action functional. Its mean is always positive. This is both supported by a Boltzmann type analysis by counting the change in phase space extension corresponding to the macrostate as by various examples of nonequilibrium models. As the Gibbsian set-up allows for …

Thermodynamics of the glassy state: effective temperature as an additional system parameter

A system is glassy when the observation time is much smaller than the equilibration time. A unifying thermodynamic picture of the glassy state is presented. Slow configurational modes are in quasi-equilibrium at an effective temperature. It enters thermodynamic relations with the configurational entropy as conjugate variable. Slow fluctuations contribute to susceptibilities via quasi-equilibrium relations, while there is also a configurational term. Fluctuation-dissipation relations also involve the effective temperature. Fluctuations in the energy are non-universal, however. The picture is su…

电子-光子混合系统的全计数统计：联合统计与涨落对称性

Full counting statistics of electron-photon hybrid systems: Joint statistics and fluctuation symmetry

本研究通过量子Lindblad主方程结合计数场，研究双量子点-光学腔混合系统中电子与光子电流的联合全计数统计，揭示大耦合下偏离二次标度律，并修正光子耗散建模以满足涨落对称性。

Thermal Fluctuations of Singular Bar-Joint Mechanisms

A bar-joint mechanism is a deformable assembly of freely rotating joints connected by stiff bars. Here we develop a formalism to study the equilibration of common bar-joint mechanisms with a thermal bath. When the constraints in a mechanism cease to be linearly independent, singularities can appear in its shape space, which is the part of its configuration space after discarding rigid motions. We show that the free-energy landscape of a mechanism at low temperatures is dominated by the neighborhoods of points that correspond to these singularities. We consider two example mechanisms with shape…

Joint probability distributions and fluctuation theorems

We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation-dissipation relations recently generalised to non-equilibrium steady-states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctua…

Universal fluctuation of polygonal crack geometry in solidified lava

Outcrops of columnar joints made of solidified lava flows are often covered by semi-ordered polygonal cracks. The polygon diameters are fairly uniform at each outcrop, but their shapes largely vary in the number of sides and internal angles. Herein, we unveil that the statistical variation in the polygon shape follows an extreme value distribution class: the Gumbel distribution. The Gumbel law was found to hold for different columnar joints, regardless of the locality, lithologic composition, and typical diameter. A common distribution for columnar joints implies a new universal class that may…