Properties of the dissipation functions for passive and active systems

Abstract

The dissipation function for a system is defined as the natural logarithm of the ratio between probabilities of a trajectory and its time-reversed trajectory, and its probability distribution follows a well-known relation called the fluctuation theorem. Using the generic Langevin equations, we derive the expressions of the dissipation function for passive and active systems. For passive systems, the dissipation function depends only on the initial and the final values of the dynamical variables of the system, not on the trajectory of the system. Furthermore, it does not depend explicitly on the reactive or dissipative coupling coefficients of the generic Langevin equations. In addition, we study a 1D case numerically to verify the fluctuation theorem with the form of the dissipation function we obtained. For active systems, we define the work done by active forces along a trajectory. If the probability distribution of the dynamical variables is symmetric under time reversal, in both cases, the average rate of change of the dissipation function with trajectory duration is nothing but the average entropy production rate of the system and reservoir.

arXiv comment15 pages, 1 figure, to be published in PRE: https://journals.aps.org/pre/accepted/0407dRddJbf18e22c1d416f26306d34d1bbb85135

References in corpus (19)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Emergence of macroscopic directed motion in populations of motile colloids
• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential
• Flocking at a distance in active granular matter
• Fluctuation Theorems
• Comparison of far-from-equilibrium work relations
• Long-range Ordering of Vibrated Polar Disks
• Symmetries in Fluctuations Far from Equilibrium
• Symmetry properties of the large-deviation function of the velocity of a self-propelled polar particle
• Rules of calculus in the path integral representation of white noise Langevin equations: the Onsager-Machlup approach
• Dynamical symmetries of Markov processes with multiplicative white noise
• Anisotropic Isometric Fluctuation Relations in experiment and theory on a self-propelled rod
• Heat and Fluctuations from Order to Chaos
• Inertia drives a flocking phase transition in viscous active fluids
• Fluctuation relations for anisotropic systems
• Out-of-equilibrium microrheology using optical tweezers to probe directional viscoelastic properties under shear