Perturbative expansion of irreversible works in symmetric and asymmetric processes
arXiv:2201.03693 · doi:10.1103/PhysRevE.106.014145
Abstract
The systematic expansion method of the solution of the Fokker-Planck equation is developed by generalizing the formulation proposed in [J. Phys. A50, 325001 (2017)]. Using this method, we obtain a new formula to calculate the mean work perturbatively which is applicable to systems with degeneracy in the eigenvalues of the Fokker-Planck operator. This method enables us to study how the geometrical symmetry affects thermodynamic description of a Brownian particle. To illustrate the application of the derived theory, we consider the Fokker-Planck equation with a two-dimensional harmonic potential. To investigate the effect of symmetry of the potential, we study thermodynamic properties in symmetric and asymmetric deformation processes of the potential: the rotational symmetry of the harmonic potential is held in the former, but it is broken in the latter. Optimized deformations in these processes are defined by minimizing mean works. Comparing these optimized processes, we find that the difference between the symmetric and asymmetric processes is maximized when the deformation time of the potential is given by a critical time which is characterized by the relaxation time of the Fokker-Planck equation. This critical time in the mean work is smaller than that of the change of the mean energy because of the hysteresis effect in the irreversible processes.
40 pages, 6 figures and 2 tables, typos were corrected
References in corpus (16)
- Making Sense of Non-Hermitian Hamiltonians
- Artificial Brownian motors: Controlling transport on the nanoscale
- Efficiency at maximum power: An analytically solvable model for stochastic heat engines
- Optimal finite-time processes in stochastic thermodynamics
- Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle
- Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
- An all-optical nanomechanical heat engine
- Work and heat probability distribution of an optically driven Brownian particle: Theory and experiments
- Optimal driving of isothermal processes close to equilibrium
- Exactly solvable model of stochastic heat engine: Optimization of power, its fluctuations and efficiency
- Computing the optimal protocol for finite-time processes in stochastic thermodynamics
- Response theory: a trajectory-based approach
- Work distribution for the driven harmonic oscillator with time-dependent strength: Exact solution and slow driving
- Work distribution in time-dependent logarithmic-harmonic potential: exact results and asymptotic analysis
- Engineered Swift Equilibration of a Brownian Gyrator
- Minimal Work Principle and its Limits for Classical Systems