Session M55: Statistical and Nonlinear Physics I

Experimental Test of the Kelvin Relation Far from Equilibrium

The Kelvin relation (KR), expressed as  π = αT, relates the Peltier Coefficient (π ), thermopower (α) and absolute temperature (T) in thermoelectric (TE) physics. The KR is a specific case of an Onsager Reciprocal Relation (ORR), a cornerstone principle in nonequilibrium thermodynamics. The derivation of the ORR, and therefore KR, explicitly assumes “near-equilibrium” conditions via the local equilibrium assumption (LEA). It remains unknown to what extent the KR may remain applicable for TE systems in “far-from-equilibrium” conditions where use of the LEA becomes questionable. We will present an experimental investigation of the KR beyond the near-equilibrium regime by directly measuring the ratio (π /α) and relating it to T in a set of thermopiles using doped silicon “nano blades” (80 nm wide x 350 nm tall x 700 nm long) as the TE elements. The experimental protocol used temperature gradients large enough that 10-40% deviations could be expected compared to theoretical values dependent on strict validity of the LEA. Our empirical results show relative deviations   |(π /α) – T|/T <2%, within the experimental uncertainty. This suggests the KR and by extension the ORR may continue to be quantitatively correct well beyond the near-equilibrium conditions assumed in their derivation.    

Time Reversal in Doi-Peliti Field Theory for Chemical Reaction Networks

We develop the Doi-Peliti field theoretic description of classical particles undergoing diffusion and chemical reaction, while coupled to thermal and chemical reservoirs.  These particles are also subject to a local, time-varying potential, through which work is done on the system.  Under the combined effects of time reversal and a gauge-like transformation of the fields, the action for this spatially-extended chemical reaction network is invariant apart from a generated work term.  Using this transformation we are able to derive Jarzyski and Crooks relations, as well as a nonequilibrium generalization of the fluctuation-dissipation relation and a heirarchy of additional formal identities.   

Anomalous thermal relaxation dynamics in a Maxwell demon setup

The Mpemba effect, an example of anomalous thermal relaxations, occurs when a system prepared at a hot temperature overtakes an identical system prepared at a warm temperature and cools down faster to the environment's temperature. Typically, the studies have focused on finding initial conditions (temperatures) that allow such a relaxation shortcut. Here, we study the role of the dynamics in the Mpemba effect.  Moreover, we focus on the Strong Mpemba effect, which occurs when there is a jump in the relaxation time of the system. Our paradigms are three- and four-level Markov jump processes, whose relaxation dynamics we vary in a way that conserves detailed balance.  In particular, for the three-level system, we show that the phase space regions with the Strong Mpemba effect in cooling and heating are non-overlapping and that there is, at most, a single Strong Mpemba temperature. In addition, as an application, we illustrate our results on a Maxwell demon setup. We show that one can utilize the Strong Mpemba effect to obtain shorter cycles of the Maxwell demon device, leading to increased power output and stable device operation. This can be done without sacrificing the efficiency of the device, thus creating efficient erasers and heat engines. 

Role of Topology in Relaxation of One-Dimensional Stochastic Processes

Stochastic processes describe dynamics of a wide variety of nonequilibrium phenomena, including chemical reaction, molecular motor and biological motion. In particular, master equations are often used to describe the dynamics of Markov processes and can be regarded as non-Hermitian Schrödinger equations.

In this talk, we will see the topological characterization of relaxation phenomena of one-dimensional stochastic processes with the aid of recent studies on the spectral theory of non-Hermitian topological phases accompanied by the non-Hermitian skin effect. To this end, we define a winding number of a master equation under the periodic boundary condition and theoretically show that it corresponds to a nonzero spectral gap under the open boundary condition (OBC) in the thermodynamic limit. We numerically confirm that the winding number corresponds to the system-size dependence of the divergent OBC relaxation time and the unconventional transient behavior called a cutoff phenomenon, where the relaxation does not occur until a certain time and then rapidly proceeds. These unconventional relaxation phenomena can be understood in terms of the so-called gap-discrepancy problems.   

Detection of a Rényi Index Dependent Transition in Entanglement Entropy Scaling

The scaling of the von Neumann entanglement entropy in d-dimensional quantum systems with the size L of a spatial partition provides essential information about the underlying phases, such as different topological and critical phases. Measuring the von Neumann entanglement entropy in experiments and quantum Monte Carlo simulations is very costly. Instead, a lower bond, namely the second Rényi entropy, can be accessed using two copies of the system (the replica trick), where in many quantum systems, it demonstrates similar scaling to the von Neumann entanglement entropy. However, Sugino and Korepiny (Int. J. Mod. Phys. B 32, 1850306 (2018)) revealed that in the ground state of some spin models, the scaling of the von Neumann and second Rényi entropies varies from power law to logarithmic scaling. We show that in the presence of conservation laws (symmetry), a quantum many-body state can be constructed with such distinct entropy scaling. Also, we demonstrate that having access to the second Rényi entropy and its symmetry resolution provides an alternative entropy measure as a lower bound on the corresponding von Neumann entanglement entropy. We show that such a symmetry-resolved measure is capable of indicating the presence of such distinct entropy scaling if associated with the targeted symmetry.   

Numerical exploration of the physical origin of eigenstate thermalization

The eigenstate thermalization hypothesis (ETH) formulated by Deutsch and Srednicki proposes that under the absence of integrability, a generic eigenstate of an isolated, interacting quantum system behaves as a thermal bath to its subsystems. In this talk, we present numerical results on a random spin-1/2 lattice with local couplings to understand the mechanism of eigenstate thermalization on a more fundamental level. We explore the mechanism by which individual eigenstates can exhibit thermal properties and connect it to the behavior of the reduced density matrix of a small subsystem.   

Towards a more fundamental understanding of eigenstate thermalization

The eigenstate thermalization hypothesis (ETH) connects the field of statistical physics with quantum mechanics. It suggests that an eigenstate of a quantum many-body system acts as a (micro)canonical ensemble for small local subsystems. In this presentation, we discuss how it can be understood more fundamentally by employing concepts from random matrix theory. In particular, we report on random matrix computations for the reduced density matrix of a spin system with random couplings.