We describe some solvable models which illustrate the Jarzynski theorem and related fluctuation theorems. We consider a charged particle in the presence of magnetic field in a two dimensional harmonic well. In the first case the centre of the harmonic potential is translated with a uniform velocity, while in the other case the particle is subjected to an ac force. We show that Jarzynski identity complements Bohr-van Leeuwen theorem on the absence of diamagnetism in equilibrium classical system. PACS numbers: 05.70. Ln, 05.40. a, 05.40.Jc Most processes that occur in nature are far from equilibrium and hence cannot be treated within the framework of classical thermodynamics. The traditional nonequilibrium statistical mechanics deals with systems near equilibrium in the linear response regime. Its success has lead to the formulation of fluctuation-dissipation relation, Onsagar's reciprocity relations and the KuboGreen formulae, etc. However, very recent developments in nonequilibrium statistical mechanics have resulted in the discovery of some exact theoretical results for systems driven far away from equilibrium and are collectively called fluctuation theorems [1]. These results include entropy production theorems The concept of free energy is of central importance in statistical mechanics and thermodynamics. With the help of free energy one can calculate all the phases of a system and their physical properties. However, the free energy of the system relative to an arbitrary reference state is often difficult to determine. Jarzynski equality(JE) relates non-equilibrium quantities with equilibrium free energies [3]. In this prescription, initially the system is assumed to be in equilibrium state determined by a thermodynamic parameter A defined by a control parameter λ A and is kept in contact with a heat bath at temperature T. The nonequilibrium process is obtained by changing the thermodynamic control parameter λ in a finite time τ according to a prescribed protocol λ(t), from λ A = λ(t=0) to some final value λ B = λ(t = τ ). The final state of the system at time τ (at the end of the protocol) will in general not be at equilibrium. It will equilibrate to a final state B(≡ λ B ) if it is further allowed to evolve by keeping parameter λ B fixed. JE states thatWhere ∆F is the free energy difference between equilibrium states A and B. Angular bracket ... denotes the average taken over different realizations for fixed protocol λ(t). W is work expended during each repetation of the protocol and is a realization dependent random variable. Jarzynski's theorem has been derived using various methods with different system dynamics [3][4][5]8]. This remarkable identity provides a practical tool to determine equilibrium thermodynamic potentials from processes carried out arbitrarily far away from equilibrium. This identity has been used to extract equilibrium free energy differences in experiments. Work distributions have been calculated analytically for several model systems and tested against various fluctuati...

a b s t r a c tWe study a periodically driven (symmetric as well as asymmetric) double-well potential system at finite temperature. We show that mean heat loss by the system to the environment (bath) per period of the applied field is a good quantifier of stochastic resonance. It is found that the heat fluctuations over a single period are always larger than the work fluctuations. The observed distributions of work and heat exhibit pronounced asymmetry near resonance. The heat loss over a large number of periods satisfies the conventional steady-state fluctuation theorem.

The correction of errors during transcription involves the diffusive backward translocation (backtracking) of RNA polymerases (RNAPs) on the DNA. A trailing RNAP on the same template can interfere with backtracking as it progressively restricts the space that is available for backward translocation and thereby ratchets the backtracked RNAP forward. We analyze the resulting negative impact on proofreading theoretically using a driven lattice gas model of transcription under conditions of dense RNAP traffic. The fraction of errors that are corrected is calculated exactly for the case of a single RNAP; for multi-RNAP transcription, we use simulations and an analytical approximation and find a decrease with increasing traffic density. Moreover, we ask how the parameters of the system have to be set to keep down the impact of the interference of a trailing RNAP. Our analysis uncovers a surprisingly simple picture of the design of the error correction system: its efficiency is essentially determined by the rate for the initial backtracking step, while the value of the cleavage rate ensures that the correction mechanism remains efficient at high transcription rates. Finally, we argue that our analysis can also be applied to cases with transcription-translation coupling where the leading ribosome on the transcript assumes the role of the trailing RNAP.

We study an asymmetric exclusion model with one dynamic roadblock particle. The roadblock particle is allowed to move diffusively as well as by longrange jumps mimicking an unbinding/rebinding process. Using Monte Carlo simulations and analytical arguments, the two types of roadblock moves are considered both separately and in combination. Several interesting dynamic phenomena are observed. The long-range jumps of the roadblock lead to a current that depends on the number of particles in the system rather than on the particle density, and thus scales linearly with the system size (up to a critical size). This behavior can be explained by a collective motion of all particles following the roadblock. The diffusive roadblock movements on the other hand lead to a ratcheting motion with the active (driven) particles pushing the roadblock forward.

Transcription by RNA polymerases is frequently interrupted by pauses. One mechanism of such pauses is backtracking, where the RNA polymerase translocates backward with respect to both the DNA template and the RNA transcript, without shortening the transcript. Backtracked RNA polymerases move in a diffusive fashion and can return to active transcription either by diffusive return to the position where backtracking was initiated or by cleaving the transcript. The latter process also provides a mechanism for proofreading. Here we present some exact results for a kinetic model of backtracking and analyse its impact on the speed and the accuracy of transcription. We show that proofreading through backtracking is different from the classical (Hopfield-Ninio) scheme of kinetic proofreading. Our analysis also suggests that, in addition to contributing to the accuracy of transcription, backtracking may have a second effect: it attenuates the slow down of transcription that arises as a side effect of discriminating between correct and incorrect nucleotides based on the stepping rates.