Narrow Results

We introduce a quantum stochastic dynamics for heat conduction. A multi-level subsystem is coupled to reservoirs at different temperatures. Energy quanta are detected in the reservoirs allowing the study of steady state fluctuations of the entropy dissipation. Our main result states a symmetry in its large deviation rate function.

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such decoupling conditions arise naturally in multifractal analysis, in Gibbs states with hard-core interactions, and in the statistics of repeated quantum measurement processes. We also prove the LDP for the entropy production of pairs of such measures and derive the related Fluctuation Relation. The proofs are based on Ruelle–Lanford functions, and the exposition is essentially self-contained.

The steady-state work fluctuations for an overdamped Brownian particle driven by an external stochastic force are analyzed by using the Langevin approach. The first two moments of the work distribution are given analytically, both are proportional to the time duration of the work injection. The first two moments determine a unique Gaussian function, and the deviations of the probability density functions (PDFs) of work from the Gaussian functions are measured. The tails of the PDFs are shown to approximate the Gaussian functions. In the limit of weak external force and large time interval, the PDF can be approximated by the Gaussian form and the steady-state fluctuation theorem is held.

The well-known Bohr–van Leeuwen Theorem states that the orbital diamagnetism of classical charged particles is identically zero in equilibrium. However, results based on real space–time approach using the classical Langevin equation predicts non-zero diamagnetism for classical unbounded (finite or infinite) systems. Here we show that the recently discovered Fluctuation Theorems, namely, the Jarzynski Equality or the Crooks Fluctuation Theorem surprisingly predicts a free energy that depends on magnetic field as well as on the friction coefficient, in outright contradiction to the canonical equilibrium results. However, in the cases where the Langevin approach is consistent with the equilibrium results, the Fluctuation Theorems lead to results in conformity with equilibrium statistical mechanics. The latter is demonstrated analytically through a simple example that has been discussed recently.

The notion of temperature in out-of-equilibrium systems is still elusive. Here, we explore three different temperature definitions for an athermal tracer immersed in a out-of-equilibrium bath of active Brownian particles, with which it interacts solely through collisions. Temperatures are, respectively, defined from velocity fluctuations, the fluctuation-dissipation theorem and a heat fluctuation theorem, and we find their values to increase with the tracer’s mass following sigmoidal trends, the first two sharing similar values, the one defined from the fluctuation theorem showing lower ones. Notably, these trends are reminiscent of the trend of the kinetic temperature of a single free active particle as function of its mass. Using thus the latter as fit functional form, we interpret the tracer as effectively behaving like a single free active particle with the same mass but lower persistence time or activity amplitude.

The effects of external torque on the F₁-ATPase rotary molecular motor are studied from the viewpoint of recent advances in stochastic thermodynamics. This motor is modeled in terms of discrete-state and continuous-state stochastic processes. The dependence of the discrete-state description on external torque and friction is obtained by fitting its transition rates to a continuous-angle model based on Newtonian mechanics with Langevin fluctuating forces and reproducing experimental data on this motor. In this approach, the continuous-angle model is coarse-grained into discrete states separated by both mechanical and chemical transitions. The resulting discrete-state model allows us to identify the regime of tight chemomechanical coupling of the F₁ motor and to infer that its chemical and mechanical efficiencies may reach values close to the thermodynamically allowed maxima near the stalling torque. We also show that, under physiological conditions, the F₁ motor is functioning in a highly-nonlinear-response regime, providing a rotation rate a million times faster than would be possible in the linear-response regime of nonequilibrium thermodynamics. Furthermore, the counting statistics of fluctuations can be obtained in the tight-coupling regime thanks to the discrete-state stochastic process and we demonstrate that the so-called fluctuation theorem provides a useful method for measuring the thermodynamic forces driving the motor out of equilibrium.

Fluctuations in the spatial position of a probe particle that is driven far from equilibrium can provide valuable information about the driving force. Analysis of the position fluctuation is through the fluctuation theorem (FT) and a generalized detailed balance called Bier-Astumian relation (BA). Here we show the usefulness of the BA for mapping potential landscapes of a particle confined in a potential field. We also demonstrate how the FT can be used to extract the driving force for a particle driven by a constant force.

We explore the fluctuation theorem for a diffusion in a tilted washboard potential where both the quantum tunneling and the thermal activation play a role. The diffusion process is treated as a biased random walk where the transition rates are enhanced due to the quantum tunneling. Within this framework, the dissipation is easy to handle, since we need not to measure the experimentally inaccessible quantity like total Hamiltonian which includes the bath degrees of freedom.

We study the full counting statistics for multi-terminal quantum dots. We show that the microscopic reversibility naturally results in a symmetry of the cumulant generating function, which generalizes the fluctuation theorem in the context of the coherent quantum transport. Using this symmetry, we derive the fluctuation-dissipation theorem and the Onsager-Casimir relation in the linear transport regime and the universal relations among nonlinear transport coefficients.