2014/06/27 by Kwangmoo Kim, Chulan Kwon, Hyunggyu Park · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boltzmann constant #Brownian motion #Canonical ensemble #Fluctuation theorem #Heat transfer #Limit (mathematics) #Mathematical analysis #Mathematics #Microcanonical ensemble #Monte Carlo method #Non-equilibrium thermodynamics #Physics #Quantum mechanics #Rare events #Saddle point #Statistical physics #Statistics #Thermal Radiation and Cooling Technologies #Thermal reservoir #Thermodynamic limit #Thermodynamics #Work (physics) #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.90.032117
published as Phys. Rev. E 90, 032117 (2014) · 12 pages
arxiv created 2014/06/27 · openalex publication_date 2014/09/16 · arxiv updated 2015/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Time-integrated quantities such as work and heat increase incessantly in time during nonequilibrium processes near steady states. In the long-time limit, the average values of work and heat become asymptotically equivalent to each other, since they only differ by a finite energy change in average. However, the fluctuation theorem (FT) for the heat is found not to hold with the equilibrium initial ensemble, while the FT for the work holds. This reveals an intriguing effect of everlasting initial memory stored in rare events. We revisit the problem of a Brownian particle in a harmonic potential dragged with a constant velocity, which is in contact with a thermal reservoir. The heat and work fluctuations are investigated with initial Boltzmann ensembles at temperatures generally different from the reservoir temperature. We find that, in the infinite-time limit, the FT for the work is fully recovered for arbitrary initial temperatures, while the heat fluctuations significantly deviate from the FT characteristics except for the infinite initial-temperature limit (a uniform initial ensemble). Furthermore, we succeed in calculating finite-time corrections to the heat and work distributions analytically, using the modified saddle point integral method recently developed by us. Interestingly, we find noncommutativity between the infinite-time limit and the infinite-initial-temperature limit for the probability distribution function (PDF) of the heat.