Heat and work distributions for mixed Gauss-Cauchy process

Abstract

We analyze energetics of a non-Gaussian process described by a stochastic differential equation of the Langevin type. The process represents a paradigmatic model of a nonequilibrium system subject to thermal fluctuations and additional external noise, with both sources of perturbations considered as additive and statistically independent forcings. We define thermodynamic quantities for trajectories of the process and analyze contributions to mechanical work and heat. As a working example we consider a particle subjected to a drag force and two independent Levy white noises with stability indices $\alpha =2$ and $\alpha =1$. The fluctuations of dissipated energy (heat) and distribution of work performed by the force acting on the system are addressed by examining contributions of Cauchy fluctuations to either bath or external force acting on the system.

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• Lévy flights versus Lévy walks in bounded domains
• On the stochastic thermodynamics of fractional Brownian motion
• Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations
• Underdamped stochastic harmonic oscillator
• The Heat Distribution of the Underdamped Langevin Equation
• Lévy flights and Lévy walks under stochastic resetting
• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Peculiarities of escape kinetics in the presence of athermal noises
• Underdamped, anomalous kinetics in double-well potentials
• Nonlinear friction in underdamped anharmonic stochastic oscillators
• Heat fluctuations in the logarithm-harmonic potential
• Heat Distribution of Relativistic Brownian Motion