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Register a new userThermodynamic large fluctuations from uniformized dynamics
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David Andrieux
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Large fluctuations have received considerable attention as they encode information on the fine-scale dynamics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermodynamical properties. Here we report that, using the technique of uniformization, the thermodynamic large deviation functions of continuous-time Markov processes can be obtained from Markov chains evolving in discrete time. This formulation offers new theoretical and numerical approaches to explore large deviation properties. In particular, the time evolution of autonomous and non-autonomous processes can be expressed in terms of a single Poisson rate. In this way the uniformization procedure leads to a simple and efficient way to simulate stochastic trajectories that reproduce the exact fluxes statistics. We illustrate the formalism for the current fluctuations in a stochastic pump model.
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Thermodynamic uncertainty relation (TUR) provides a stricter bound for entropy production (EP) than that of the thermodynamic second law. This stricter bound can be utilized to infer the EP and derive other trade-off relations. Though the validity of the TUR has been verified in various stochastic systems, its application to general Langevin dynamics has not been successful in a unified way, especially for underdamped Langevin dynamics, where odd parity variables in time-reversal operation such as velocity get involved. Previous TURs for underdamped Langevin dynamics is neither experimentally accessible nor reduced to the original form of the overdamped Langevin dynamics in the zero-mass limit. Here, we find an operationally accessible TUR for underdamped Langevin dynamics with an arbitrary time-dependent protocol. We show that the original TUR is a consequence of our underdamped TUR in the zero-mass limit. This indicates that the TUR formulation presented here can be regarded as the universal form of the TUR for general Langevin dynamics. The validity of our result is examined and confirmed for three prototypical underdamped Langevin systems and their zero-mass limits; free diffusion dynamics, charged Brownian particle in a magnetic field, and molecular refrigerator.
We study the fluctuations of the Gaussian model, with conservation of the order parameter, evolving in contact with a thermal bath quenched from inverse temperature $beta _i$ to a final one $beta _f$. At every time there exists a critical value $s_c(t)$ of the variance $s$ of the order parameter per degree of freedom such that the fluctuations with $s>s_c(t)$ are characterized by a macroscopic contribution of the zero wavevector mode, similarly to what occurs in an ordinary condensation transition. We show that the probability of fluctuations with $s<inf_t [s_c(t)]$, for which condensation never occurs, rapidly converges towards a stationary behavior. By contrast, the process of populating the zero wavevector mode of the variance, which takes place for $s>inf _t [s_c(t)]$, induces a slow non-equilibrium dynamics resembling that of systems quenched across a phase transition.
We study the dynamics of the fluctuations of the variance $s$ of the order parameter of the Gaussian model, following a temperature quench of the thermal bath. At each time $t$, there is a critical value $s_c(t)$ of $s$ such that fluctuations with $s>s_c(t)$ are realized by condensed configurations of the systems, i.e., a single degree of freedom contributes macroscopically to $s$. This phenomenon, which is closely related to the usual condensation occurring on average quantities, is usually referred to as {it condensation of fluctuations}. We show that the probability of fluctuations with $s<inf_t [s_c(t)]$, associated to configurations that never condense, after the quench converges rapidly and in an adiabatic way towards the new equilibrium value. The probability of fluctuations with $s>inf_t [s_c(t)]$, instead, displays a slow and more complex behavior, because the macroscopic population of the condensing degree of freedom is involved.
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