Colored thermal noise driven dynamical system in the presence and absence of non-equilibrium constraint: time dependence of information entropy flux and entropy production

Semiconductor laser systems excited by multiplicative Ornstein-Uhlenbeck noise and additive sine-Wiener noise in relation to real and imaginary parts

In this paper we study a semiconductor laser system excited by multiplicative Ornstein-Uhlenbeck (OU) noise and additive sine-Wiener (SW) noise with a related real part and imaginary part. The two-dimensional Langevin equation (LE) with cross-correlating complex OU noise and complex SW noise is equivalent to the six-dimensional LE. Based on functional methods and spatial dimension extension methods, the six-dimensional Fokker-Planck equation (FPE) is achieved. Through Taylor expansion approximation and linear transformation, the dimensionality of FPE is reduced, and the exact expression of the probability distribution (SPD) in steady state is obtained. The impacts of noise parameters on laser intensity on SPD are further analyzed. Moreover, based on the reduced FPE, the information entropy of the system is obtained. This calculation is useful for us to understand further the influence of system parameters and noise correlation coefficient on the system. The main work lies in obtaining an alternative method for deriving a FPE corresponding to the two-dimensional stochastic semiconductor laser model, which is more applicable than methods in previous literature. An equivalent expression for cross-correlated OU noise and cross-correlated SW noise as well as a method for approximate solutions of a high-dimensional FPE are also provided.

Unified approach to stochastic thermodynamics: Application to a quantum heat engine

In the present study we have developed an alternative formulation for the quantum stochastic thermodynamics based on the c-number Langevin equation for the system-reservoir model. This is analogous to the classical one. Here we have considered both Markovian and non-Markovian dynamics (NMD). Consideration of the NMD is an important issue at the current state of the stochastic thermodynamics. Applying the present formalism, we have carried out a comparative study on the heat absorbed and the change of entropy with time for a linear quantum system and its classical analog for both Markovian and NMD. Here the strength of the thermal noise and its correlation time for the respective cases are the leading quantities to explain any distinguishable feature which may appear with the equilibration kinetics. For another application, we have proposed a formulation with classical look for a quantum stochastic heat engine. Using it we have presented a comparative study on the efficiency and its value at maximum power for a quantum stochastic heat engine and its classical analog. The engines are Carnot like which are coupled with their respective Markovian thermal baths. Here also the noise strength as well as the diffusion constant are the leading quantities to explain any noticeable feature.

Shannon entropic temperature and its lower and upper bounds for non-Markovian stochastic dynamics

In this article we have studied Shannon entropic nonequilibrium temperature (NET) extensively for a system which is coupled to a thermal bath that may be Markovian or non-Markovian in nature. Using the phase-space distribution function, i.e., the solution of the generalized Fokker Planck equation, we have calculated the entropy production, NET, and their bounds. Other thermodynamic properties like internal energy of the system, heat, and work, etc. are also measured to study their relations with NET. The present study reveals that the heat flux is proportional to the difference between the temperature of the thermal bath and the nonequilibrium temperature of the system. It also reveals that heat capacity at nonequilibrium state is independent of both NET and time. Furthermore, we have demonstrated the time variations of the above-mentioned and related quantities to differentiate between the equilibration processes for the coupling of the system with the Markovian and the non-Markovian thermal baths, respectively. It implies that in contrast to the Markovian case, a certain time is required to develop maximum interaction between the system and the non-Markovian thermal bath (NMTB). It also implies that longer relaxation time is needed for a NMTB compared to a Markovian one. Quasidynamical behavior of the NMTB introduces an oscillation in the variation of properties with time. Finally, we have demonstrated how the nonequilibrium state is affected by the memory time of the thermal bath.

Stationary and dynamical properties of information entropies in nonextensive systems

The Tsallis entropy and Fisher information entropy (matrix) are very important quantities expressing information measures in nonextensive systems. Stationary and dynamical properties of the information entropies have been investigated in the N -unit coupled Langevin model subjected to additive and multiplicative white noise, which is one of typical nonextensive systems. We have made detailed, analytical and numerical study on the dependence of the stationary-state entropies on additive and multiplicative noise, external inputs, couplings, and number of constitutive elements (N) . By solving the Fokker-Planck equation (FPE) by both the proposed analytical scheme and the partial difference equation method, transient responses of the information entropies to an input signal and an external force have been investigated. We have calculated the information entropies also with the use of the probability distribution derived by the maximum-entropy method, whose result is compared to that obtained by the FPE. The Cramér-Rao inequality is shown to be expressed by the extended Fisher entropy, which is different from the generalized Fisher entropy obtained from the generalized Kullback-Leibler divergence in conformity with the Tsallis entropy. The effect of additive and multiplicative colored noise on information entropies is discussed also.