The analysis of fluctuations generated by a thermal reservoir has produced many results throughout the history of science, ranging from the verification of the atomic hypothesis, running through critical phenomena to the most recent advances in the description of non-equilibrium thermodynamic processes. Motivated by recent theoretical and experimental works, we analyze the non-equilibrium and equilibrium fluctuations caused by a finite and chaotic heat bath in a simple system of interest. Finite bath and system of interest give rise to a non-ergodic composite system when interacting with each other. We have characterized the equilibrium distribution induced by the finite bath and numerically verified the finite-bath fluctuation theorem. We have also verified the convergence of our results to Crooks' fluctuation theorem as the number of degrees of freedom of the finite bath increases while the non-ergodic character remains.
Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: An exactly solvable non-dissipative non-ergodic model
Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath
Szkoła Doktorska Nauk Ścisłych i Przyrodniczych, Uniwersytet Jagielloński（雅盖隆大学自然科学博士学院）；Instytut Fizyki Teoretycznej, Wydział Fizyki, Astronomii i Informatyki Stosowanej, Uniwersytet Jagielloński（雅盖隆大学物理、天文学与应用信息学系理论物理研究所）；Univ. Toulouse, CNRS, Laboratoire de Physique Théorique（图卢兹大学，法国国家科学研究中心，理论物理实验室）；Mark Kac Complex Systems Research Center, Jagiellonian University in Krakow（克拉科夫雅盖隆大学马克·卡克复杂系统研究中心）
The presence of symmetries in a closed many-body quantum system results in integrability. For such integrable systems, complete thermalization does not occur. As a result, the system remains non-ergodic. On the other hand, a set of non-interacting atoms connected to a regular bosonic bath thermalizes. Here, we show that such atoms in a spatially-correlated thermal bath can show both the behavior depending on the temperature. At zero temperature, the bath has a large correlation length, and hence it acts as a common environment. In this condition, a set of weak symmetries exist, which prevent t…
We study a quantum spin-1/2 chain that is dual to the canonical problem of non-equilibrium Kawasaki dynamics of a classical Ising chain coupled to a thermal bath. The Hamiltonian is obtained for the general disordered case with non-uniform Ising couplings. The quantum spin chain (dubbed Ising-Kawasaki) is stoquastic, and depends on the Ising couplings normalized by the bath's temperature. We give its exact ground states. Proceeding with uniform couplings, we study the one- and two-magnon excitations. Solutions for the latter are derived via a Bethe Ansatz scheme. In the antiferromagnetic regim…
A note on Harris' ergodic theorem, controllability and perturbations of harmonic networks
我们表明，控制理论的元素，再加上哈里斯遍历定理的应用，提供了一种替代方法，显示指数收敛到一个独特的固定措施的某些类的网络耦合到热浴的准谐波经典振荡器。对于以$\mathbf{R}^d$中的$\mathrm{d} X_t = A X_t \,\mathrm{d} t + F(X_t) \,\mathrm{d} t + B \,\mathrm{d} W_t$形式表示的振子系统，其中$A$编码力的谐波部分，而$-F$对应于势的非谐波部分的梯度，我们获得指数混合的假设如下：$A$是耗散的，对$(A,B)$满足卡尔曼条件，$F$在无穷远处增长得足够慢（取决于$d$的维数），并且运动方程中的矢量场至少在相空间的一点上满足弱赫曼德条件。
We analyze the dynamics of a passive colloidal probe immersed in an active bath using an optical trap to study three physical processes: (1) the non-equilibrium fluctuations transferred to the probe by the active bath, (2) the friction experienced by the probe as it is driven through the active bath, and (3) the force relaxation of the probe returning to its equilibrium position. We measure the local force dynamics where all of the following characteristics are of $\mathcal{O}(1)$: the size of the probe colloid relative to active bath particle; the size of the probe colloid relative to the cha…
