Entropy production theorem for a charged particle in an electromagnetic field

Irreversibility of stochastic state transitions in Langevin systems with odd elasticity

Active microscopic objects, such as an enzyme molecule, are modeled by the Langevin system with the odd elasticity, in which energy injection from the substrate to the enzyme is described by the antisymmetric part of the elastic matrix. By applying the Onsager-Machlup integral and large deviation theory to the Langevin system with odd elasticity, we can calculate the cumulant generating function of the irreversibility of the state transition. For an N-component system, we obtain a formal expression of the cumulant generating function and demonstrate that the oddness λ, which quantifies the antisymmetric part of the elastic matrix, leads to higher-order cumulants that do not appear in a passive elastic system. To demonstrate the effect of the oddness under the concrete parameter, we analyze the simplest two-component system and obtain the optimal transition path and cumulant generating function. The cumulants obtained from expansion of the cumulant generating function increase monotonically with the oddness. This implies that the oddness causes the uncertainty of stochastic state transitions.

Fluctuation theorem for irreversible entropy production in electrical conduction

Linear irreversible thermodynamics predicts that the entropy production rate can become negative. We demonstrate this prediction for metals under AC driving whose conductivity is well described by the Drude-Sommerfeld model. We then show that these negative rates are fully compatible with stochastic thermodynamics, namely, that the entropy production does fulfill a fluctuation theorem. The analysis is concluded with the observation that the stochastic entropy production as defined by the surprisal or ignorance of the Shannon information does not agree with the phenomenological approach.

Time-reversal symmetry for systems in a constant external magnetic field

The time-reversal properties of charged systems in a constant external magnetic field are reconsidered in this paper. We show that the evolution equations of the system are invariant under a new symmetry operation that implies a new signature property for time-correlation functions under time reversal. We then show how these findings can be combined with a previously identified symmetry to determine, for example, null components of the correlation functions of velocities and currents and of the associated transport coefficients. These theoretical predictions are illustrated by molecular dynamics simulations of superionic AgI.

Non-Markovian barotropic-type and Hall-type fluctuation relations in crossed electric and magnetic fields

In this paper we derive the non-Markovian barotropic-type and Hall-type fluctuation relations for noninteracting charged Brownian particles embedded in a memory heat bath and under the action of crossed electric and magnetic fields. We first obtain a more general non-Markovian fluctuation relation formulated within the context of a generalized Langevin equation with arbitrary friction memory kernel and under the action of a constant magnetic field and an arbitrary time-dependent electric field. It is shown that this fluctuation relation is related to the total amount of an effective work done on the charged particle as it is driven out of equilibrium by the applied time-dependent electric field. Both non-Markovian barotropic- and Hall-type fluctuation relations are then derived when the electric field is assumed to be also a constant vector pointing along just one axis. In the Markovian limit, we show explicitly that they reduce to the same results reported in the literature.

Non-Markovian work fluctuation theorem in crossed electric and magnetic fields

The validity of the transient work fluctuation theorem for a charged Brownian harmonic oscillator embedded in a non-Markovian heat bath and under the action of crossed electric and magnetic fields is investigated. The aforementioned theorem is verified to be valid within the context of the generalized Langevin equation with an arbitrary memory kernel and arbitrary dragging in the potential minimum. The fluctuation-dissipation relation of the second kind is assumed to be valid and shows that the non-Markovian stochastic dynamics associated with the particle, in the absence of the external time-dependent electric field, reaches an equilibrium state, as is precisely demanded by such a relation. The Jarzynski equality in this problem is also analyzed.

Shannon entropic temperature and its lower and upper bounds for non-Markovian stochastic dynamics

In this article we have studied Shannon entropic nonequilibrium temperature (NET) extensively for a system which is coupled to a thermal bath that may be Markovian or non-Markovian in nature. Using the phase-space distribution function, i.e., the solution of the generalized Fokker Planck equation, we have calculated the entropy production, NET, and their bounds. Other thermodynamic properties like internal energy of the system, heat, and work, etc. are also measured to study their relations with NET. The present study reveals that the heat flux is proportional to the difference between the temperature of the thermal bath and the nonequilibrium temperature of the system. It also reveals that heat capacity at nonequilibrium state is independent of both NET and time. Furthermore, we have demonstrated the time variations of the above-mentioned and related quantities to differentiate between the equilibration processes for the coupling of the system with the Markovian and the non-Markovian thermal baths, respectively. It implies that in contrast to the Markovian case, a certain time is required to develop maximum interaction between the system and the non-Markovian thermal bath (NMTB). It also implies that longer relaxation time is needed for a NMTB compared to a Markovian one. Quasidynamical behavior of the NMTB introduces an oscillation in the variation of properties with time. Finally, we have demonstrated how the nonequilibrium state is affected by the memory time of the thermal bath.

Power fluctuation theorem for a Brownian harmonic oscillator

In this paper we study the validity of the total power fluctuation theorem spent on a Brownian harmonic oscillator when the system is driven out of equilibrium through the drag of the potential minimum. The theorem is first proved for an ordinary harmonic oscillator in two cases: The first one considers the particle in a thermal bath under the action of Gaussian white noise, and in the second one the drift is provided by an additional external Gaussian colored noise satisfying the characteristics of an Ornstein-Uhlenbeck process. We go further, by considering a charged harmonic oscillator under the action of an electromagnetic field. The theorem is also proven as in the two cases given above. In both of those cases, we illustrate the theorem for a uniform motion of the trap potential minimum and show that in the presence of external colored noise, the theorem is only valid in the stationary state.

Stochastic thermodynamics, fluctuation theorems and molecular machines

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.