Academic literature on the topic 'Conventional fluctuation-dissipation relation'

In this paper, we dwell on three issues: (1) revisit the relation between vacuum fluctuations and radiation reaction in atom-field interactions, an old issue that began in the 1970s and settled in the 1990s with its resolution recorded in monographs; (2) the fluctuation–dissipation relation (FDR) of the system, pointing out the differences between the conventional form in linear response theory (LRT) assuming ultra-weak coupling between the system and the bath, and the FDR in an equilibrated final state, relaxed from the nonequilibrium evolution of an open quantum system; (3) quantum radiation from an atom interacting with a quantum field: We begin with vacuum fluctuations in the field acting on the internal degrees of freedom (idf) of an atom, adding to its dynamics a stochastic component which engenders quantum radiation whose backreaction causes quantum dissipation in the idf of the atom. We show explicitly how different terms representing these processes appear in the equations of motion. Then, using the example of a stationary atom, we show how the absence of radiation in this simple cases is a result of complex cancellations, at a far away observation point, of the interference between emitted radiation from the atom and the local fluctuations in the free field. In so doing we point out in Issue 1 that the entity which enters into the duality relation with vacuum fluctuations is not radiation reaction, which can exist as a classical entity, but quantum dissipation. Finally, regarding issue 2, we point out for systems with many atoms, the co-existence of a set of correlation-propagation relations (CPRs) describing how the correlations between the atoms are related to the propagation of their (retarded non-Markovian) mutual influence manifesting in the quantum field. The CPR is absolutely crucial in keeping the balance of energy flows between the constituents of the system, and between the system and its environment. Without the consideration of this additional relation in tether with the FDR, dynamical self-consistency cannot be sustained. A combination of these two sets of relations forms a generalized matrix FDR relation that captures the physical essence of the interaction between an atom and a quantum field at arbitrary coupling strength.

Abstract Generalized statistical mechanics based on q-Gaussian has been demonstrated to be an effective theoretical framework for the analysis of non-equilibrium systems. Since q-generalized (non-extensive) statistical mechanics reduces the nonlinearity in the system into deformed entropy and probability distributions, we introduce an alternative method based on the time conversion method using the Loewner equation by investigating the statistical physical properties of one-dimensional stochastic dynamics described by the Langevin equation with multiplicative noise. We demonstrate that a randomized time transformation using Loewner time enables the conversion of the multiplicative Langevin dynamics into an equilibrium system obeying a conventional microcanonical ensemble. For the equilibrium Langevin system after the Loewner time conversion, the fluctuation-dissipation relation and path integral fluctuation theorem were discussed to derive the response function under a nonlinear perturbation and an extended Jarzynski equality. The present results suggest the efficacy of the introducing randomized time for analyzing non-equilibrium systems, and indicate a novel connection between q-generalized (non-extensive) and Boltzmann–Gibbs statistical mechanics.

Thermodynamic uncertainty principles make up one of the few rare anchors in the largely uncharted waters of nonequilibrium systems, the fluctuation theorems being the more familiar. In this work we aim to trace the uncertainties of thermodynamic quantities in nonequilibrium systems to their quantum origins, namely, to the quantum uncertainty principles. Our results enable us to make this categorical statement: For Gaussian systems, thermodynamic functions are functionals of the Robertson-Schrödinger uncertainty function, which is always non-negative for quantum systems, but not necessarily so for classical systems. Here, quantum refers to noncommutativity of the canonical operator pairs. From the nonequilibrium free energy, we succeeded in deriving several inequalities between certain thermodynamic quantities. They assume the same forms as those in conventional thermodynamics, but these are nonequilibrium in nature and they hold for all times and at strong coupling. In addition we show that a fluctuation-dissipation inequality exists at all times in the nonequilibrium dynamics of the system. For nonequilibrium systems which relax to an equilibrium state at late times, this fluctuation-dissipation inequality leads to the Robertson-Schrödinger uncertainty principle with the help of the Cauchy-Schwarz inequality. This work provides the microscopic quantum basis to certain important thermodynamic properties of macroscopic nonequilibrium systems.

We show that treating the black-body radiation field as a heat bath enables one to utilize powerful techniques from the realm of stochastic physics (such as the fluctuation–dissipation theorem and the related radiation damping) to treat problems that could not be treated rigorously by conventional methods. We illustrate our remarks by discussing specifically the effect of temperature on atomic spectral lines, and the solution to the problem of runaway solutions in the equation of motion of a radiating electron. We also present brief discussions relating to anomalous diffusion and wave-packet spreading in a radiation field and the influence of quantum effects on the laws of thermodynamics.PACS Nos.: 31.30.jg, 05.40.–a

In the mesoscopic world, diffusion is a ubiquitous process and it is usually explained by the Einstein’s theory of Brownian motion (BM). However, in the biological systems, some peculiar dynamical behaviors are observed as opposed to those of the BM [1,2]. Such characteristics can be understood by considering that apart from the thermal noise, the system is subjected to an additional noise called active noise stemming from some active processes such as ATP hydrolysis. Due to the presence of active noise, the system is driven out of equilibrium as it is manifested by the breakdown of the conventional fluctuation-dissipation relation (FDR). In the first part of my thesis (Chapter 1- 5), we study two activity-induced diffusive systems - (i) self-propelled particle and (ii) passive colloidal particle in the active surroundings [3]. The dynamics of a self-propelled particle is conceived through the run-and-tumble particle (RTP) model in which the active noise is taken as dichotomous (telegraphic) noise. By employing the phasespace path integral (PSPI) technique, we find that unlike free Brownian motion, the distributions at early and intermediate times are double-peaked, as has been observed experimentally [4]. On confining them in a harmonic potential, the distribution is often found to be concentrated near the boundaries. This is the trait of RTPs such as bacteria, Janus particles, as supported by many theoretical calculations and experimental evidences [5]. Another problem we deal with is the diffusive motion of a passive particle in a bath containing active particles such as bacteria, motor proteins, etc. By modelling the active bath by Gaussian colored noise (GCN), we find that the distribution is always Gaussian with an enhanced diffusivity. Similar traits have been observed in the diffusion processes of colloids in a low-dense bacterial solution [1, 6]. In many recent experiments on the dynamics of colloids inside a living cell, it has been found that the distribution has a long exponential tail [2]. By taking the active noise as Poissonian white and Poissonian colored noise (PWN and PCN), we explain the results. Also, many transient behaviors of these models are explored theoretically [3]. In the second part of my thesis (Chapter 6), we theoretically study the first passage problem of a particle which diffuses with a diffusion constant which switches between two states [7]. This model is used to investigate the target search by protein molecules along a DNA chain. By computing the survival probability, the average rate and the absorption rate, we find that (i) the particle has a better chance of survival in the presence of sinks for the switching diffusion compared to a system having single diffusivity (normal case), and (ii) the absorption rate is comparatively enhanced for the switching case at the intermediate timescale. In the long-time limit, the rate in both switching and normal diffusion are equal. We also investigate the impact of different parameters such as initial positions, Poisson rates, the strength of diffusivity. This study may be helpful to find the suitable conditions for the optimal search strategy. In the final part of my thesis (Chapter 7-9), we investigate the thermodynamic properties of a passive colloid diffusing in an active bath. We study work fluctuations in two different active baths, namely GCN and PWN baths for two different protocols [8]. Further we investigate the fluctuation relations (FR) to find that the conventional FRs of work with the ambient temperature does not hold in the transient period, as reported earlier [9], but at the steady state a certain kind of FR emerges in which the ambient temperature is replaced with an effective temperature. This is valid for both the models, and it is in sync with the one obtained experimentally by Maggi et. al. [9]. Also, in GCN model, we establish an FR analogous to the Jarzynski equality (JE) following the Hatano-Sasa formalism. Another important quantity we study is the heat fluctuations for a trapped Brownian particle in an active bath [10]. The GCN and PWN models are used separately to design the active bath. For both cases, the heat distribution is computed to find that there is a net heat flux towards the particle, and it is substantiated by an FR at the steady state. Then we compute the total entropy production which justifies the second law of thermodynamics. Our system can be used to design mesoscopic heat engine.