Heat fluctuations and initial ensembles

Abstract

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.

Heat fluctuations for underdamped Langevin dynamics

“…One can check that this identity is verified by all linear diffusion systems studied so far, both theoretically [2,7,8,[14][15][16][17] and experimentally [18,26], although it was unnoticed [27].An example is given in the Supplemental Material [24].…”

“…This gives rise to exponential tails in the pdf of Q and is signaled by the presence of singularities in the corresponding characteristic function. Such temporal "boundary" effects that take place in systems with unbounded potentials are now well-documented, both theoretically [6][7][8][9][10][11][12][13][14][15][16][17] and experimentally [18][19][20].…”

Stochastic thermodynamics of Langevin systems under time-delayed feedback control. II. Nonequilibrium steady-state fluctuations

“…The leading contribution to the LDF then comes from the singularity, which induces an exponential tail in the pdf. This issue is now well documented in the literature, both theoretically [14][15][16][17][18][19][20][21][22][23][24] and experimentally [25][26][27]. In consequence, while the three observables βW t , βQ t , and Σ t have the same expectation value, their LDFs may differ.…”

Nonequilibrium Fluctuations for a Single-Particle Analog of Gas in a Soft Wall

“…Similar experimental systems were studied, such as a molecule in the atomic force microscopy or a colloidal particle in the optical trap pulled by an external force [11], an electrical dipole driven by a small current [12], and a harmonic oscillator under an external force [13,14]. These systems are well described by the overdamped Langevin equation, and theoretical works were accompanied or performed separately [15,16]. There were also experimental studies for biological systems with unknown dynamical details, such as an RNA molecule unfolded and refolded by optical tweezers [17,18] and a rotating motor protein F 1 -ATPase [19], for which agreement with theory is less accurate.…”