Role of thermal fluctuations in biological copying mechanisms.

During transcription, translation, or self-replication of DNA or RNA, information is transferred to the newly formed species from its predecessor. These processes can be interpreted as (generalized) biological copying mechanism as the new biological entities like DNA, RNA, or proteins are representing the information of their parent bodies uniquely. The accuracy of these copying processes is essential, since errors in the copied code can reduce the functionality of the next generation. Such errors might result from perturbations on these processes. Most important in this context is the temperature of the medium, i.e., thermal noise. Although a reasonable amount of experimental studies have been carried out on this important issue, theoretical understanding is truly sparse. In the present work, we illustrate a model study which is able to focus on the effect of the temperature on the process of biological copying mechanisms, as well as on mutation. We find for our paradigmatic models that, in a quite general scenario, the copying processes are most accurate at an intermediate temperature range; i.e., there exists an optimum temperature where mutation is most unlikely. This allows us to interpret the observations for some biological species with the aid of our model study.

Stochastic resonance and hysteresis in climate with state-dependent fluctuations.

We consider two aspects in climatic science where bistability between the two stable states of the systems is observed. One is the transition between the glacial and the interglacial period in Earth's glacial cycle. Another is the thermohaline circulation in the North Atlantic ocean. Both of these phenomena can be modeled by the overdamped dynamics of a Brownian particle in a double-well potential subject to periodic forcing. For the former case, the two wells represent two different climates and the periodic forcing is sufficiently weak not to cause a transition between the two states without the effect of the noise. Whereas in case of the latter phenomenon, the two states correspond to the two different conditions of the flow and the strength of the periodic forcing is high enough to give rise to hysteresis in the system. We propose that one important component of the dynamics, short-term fluctuations related to weather, in both of these cases, depends on the current climatic state of the system. This leads to introduction of the state-dependent diffusion coefficients in the dynamics because the diffusion coefficient represents the strength of the fluctuations. We justify our argument by analyzing the δ^{18}O record for the glacial cycle model. We have shown that this consideration can produce certain features in the dynamics which agree with the real observations in case of both glacial cycles and thermohaline flow.

Logical response induced by temperature asymmetry.

It is known that the reliable logical response can be extracted from a noisy bistable system at an intermediate value of noise strength when two random or periodic, two-level, square waveform serve as the inputs. The asymmetry of the potential has a very important role and dictates the type of logical operation, such as or or and, exhibited by the system. Here we show that one can construct logic gates with symmetric bistable potential if the two states of the double-well are thermalized with two different heat baths. It has been found that if a given state is kept at a sufficiently low temperature compared to the other, the system shows one kind of logic behavior (say, or). Interestingly, the system's response turns into the other kind (say, and) if the temperature of the initial low-temperature well is increased gradually and the quality of the logical response first improves and then weakens after passing through a maximum at a particular value. However, the reliability of the second kind of logical response (and) is not as good as the first kind (or) and depends on the amplitude of the inputs. Still one can construct both kinds of logic gates with maximum reliability by properly choosing the initial low-temperature well.

Critical fluctuations and slowing down of chaos.

Fluids cooled to the liquid-vapor critical point develop system-spanning fluctuations in density that transform their visual appearance. Despite a rich phenomenology, however, there is not currently an explanation of the mechanical instability in the molecular motion at this critical point. Here, we couple techniques from nonlinear dynamics and statistical physics to analyze the emergence of this singular state. Numerical simulations and analytical models show how the ordering mechanisms of critical dynamics are measurable through the hierarchy of spatiotemporal Lyapunov vectors. A subset of unstable vectors soften near the critical point, with a marked suppression in their characteristic exponents that reflects a weakened sensitivity to initial conditions. Finite-time fluctuations in these exponents exhibit sharply peaked dynamical timescales and power law signatures of the critical dynamics. Collectively, these results are symptomatic of a critical slowing down of chaos that sits at the root of our statistical understanding of the liquid-vapor critical point.

Self-Averaging Fluctuations in the Chaoticity of Simple Fluids.

Bulk properties of equilibrium liquids are a manifestation of intermolecular forces. Here, we show how these forces imprint on dynamical fluctuations in the Lyapunov exponents for simple fluids with and without attractive forces. While the bulk of the spectrum is strongly self-averaging, the first Lyapunov exponent self-averages only weakly and at a rate that depends on the length scale of the intermolecular forces; short-range repulsive forces quantitatively dominate longer-range attractive forces, which act as a weak perturbation that slows the convergence to the thermodynamic limit. Regardless of intermolecular forces, the fluctuations in the Kolmogorov-Sinai entropy rate diverge, as one expects for an extensive quantity, and the spontaneous fluctuations of these dynamical observables obey fluctuation-dissipation-like relationships. Together, these results are a representation of the van der Waals picture of fluids and another lens through which we can view the liquid state.

Extensivity and additivity of the Kolmogorov-Sinai entropy for simple fluids.

According to the van der Waals picture, attractive and repulsive forces play distinct roles in the structure of simple fluids. Here, we examine their roles in dynamics; specifically, in the degree of deterministic chaos using the Kolmogorov-Sinai (KS) entropy rate and the spectra of Lyapunov exponents. With computer simulations of three-dimensional Lennard-Jones and Weeks-Chandler-Andersen fluids, we find repulsive forces dictate these dynamical properties, with attractive forces reducing the KS entropy at a given thermodynamic state. Regardless of interparticle forces, the maximal Lyapunov exponent is intensive for systems ranging from 200 to 2000 particles. Our finite-size scaling analysis also shows that the KS entropy is both extensive (a linear function of system-size) and additive. Both temperature and density control the "dynamical chemical potential," the rate of linear growth of the KS entropy with system size. At fixed system-size, both the KS entropy and the largest exponent exhibit a maximum as a function of density. We attribute the maxima to the competition between two effects: as particles are forced to be in closer proximity, there is an enhancement from the sharp curvature of the repulsive potential and a suppression from the diminishing free volume and particle mobility. The extensivity and additivity of the KS entropy and the intensivity of the largest Lyapunov exponent, however, hold over a range of temperatures and densities across the liquid and liquid-vapor coexistence regimes.

Landauer's blowtorch effect as a thermodynamic cross process: Brownian cooling.

The local heating of a selected region in a double-well potential alters the relative stability of the two wells and gives rise to an enhancement of population transfer to the cold well. We show that this Landauer's blowtorch effect may be considered in the spirit of a thermodynamic cross process linearly connecting the flux of particles and the thermodynamic force associated with the temperature difference and consequently ensuring the existence of a reverse cross effect. This reverse effect is realized by directing the thermalized particles in a double-well potential by application of an external bias from one well to the other, which suffers cooling.

Landauer's blow-torch effect in systems with entropic potential.

We consider local heating of a part of a two-dimensional bilobal enclosure of a varying cross section confining a system of overdamped Brownian particles. Since varying cross section in higher dimension results in an entropic potential in lower dimension, local heating alters the relative stability of the entropic states. We show that this blow-torch effect modifies the entropic potential in a significant way so that the resultant effective entropic potential carries both the features of variation of width of the confinement and variation of temperature along the direction of transport. The reduced probability distribution along the direction of transport calculated by full numerical simulations in two dimensions agrees well with our analytical findings. The extent of population transfer in the steady state quantified in terms of the integrated probability of residence of the particles in either of the two lobes exhibits interesting variation with the mean position of the heated region. Our study reveals that heating around two particular zones of a given lobe maximizes population transfer to the other.

Entropic memory erasure.

We have considered a Brownian particle confined in a two-dimensional bilobal enclosure where the state of the particle represents a bit of information having binary value 0 (left lobe) or 1 (right lobe). A time linear force is applied on the particle, driving it selectively to a particular lobe, and thus erasing one bit of information. We explore the statistics of heat and work associated with memory erasure to realize the Landauer limit in the entropic domain. Our results suggest that the mean value of work done associated with the complete erasure procedure satisfies the Landauer bound even when the memory is purely entropic in nature.

Capturing the Landauer bound through the application of a detailed Jarzynski equality for entropic memory erasure.

The states of an overdamped Brownian particle confined in a two-dimensional bilobal enclosure are considered to correspond to two binary values: 0 (left lobe) and 1 (right lobe). An ensemble of such particles represents bits of entropic information. An external bias is applied on the particles, equally distributed in two lobes, to drive them to a particular lobe erasing one kind of bit of information. It has been shown that the average work done for the entropic memory erasure process approaches the Landauer bound for a very slow erasure cycle. Furthermore, the detailed Jarzynski equality holds to a very good extent for the erasure protocol, so that the Landauer bound may be calculated irrespective of the time period of the erasure cycle in terms of the effective free-energy change for the process. The detailed Jarzynski equality applied to two subprocesses, namely the transition from entropic memory state 0 to state 1 and the transition from entropic memory state 1 to state 1, connects the work done on the system to the probability to occupy the two states under a time-reversed process. In the entire treatment, the work appears as a boundary effect of the physical confinement of the system not having a conventional potential energy barrier. Finally, an analytical derivation of the detailed and classical Jarzynski equality for Brownian movement in confined space with varying width has been proposed. Our analytical scheme supports the numerical simulations presented in this paper.

Control of logic gates by dichotomous noise in energetic and entropic systems.

We consider the stochastic response of a nonlinear dynamical system towards a combination of input signals. The response can assume binary values if the state of the system is considered to be the output and the system can make transitions between two states separated by an energetic or entropic barrier. We show how the input-output correspondence can be controlled by an external exponentially correlated dichotomous noise optimizing the logical response which exhibits a maximum at an intermediate value of correlation time. This resonance manifests itself as a "logical" resonance correlation effect and sets the condition for performance of the stochastic system as a logic gate. The role of asymmetry of the dichotomous noise is examined and the results on numerical simulations are correlated with a two-state model using a master equation approach.

Logic gates for entropic transport.

We consider a Brownian particle that is confined in a two-dimensional enclosure and driven by a combination of input signals. It has been shown that the logic gates can be formed by considering the state of the particle experiencing an entropic barrier as the output signal. For a consistent logical output, it is necessary to optimize the strength of the noise driving the particle for a given system size. The variation of the logical output behavior exhibits a turnover at an optimal value of system size parameter, implying a size resonance condition in entropic transport. The role of a transverse bias field used to tune the transport between the entropy dominated regime and the energy dominated regime is elucidated.

Dynamical hysteresis in a self-oscillating polymer gel.

An ionic polymer gel may undergo rhythmical swelling-deswelling kinetics induced by chemical oscillation. We demonstrate that the gel admits of dynamical hysteresis, which is manifested in the non-vanishing area of the response function--concentration (of reaction substrate) hysteresis loop, the response function being the integrated probability of residence of the polymer in any one of the swelled or deswelled states. The loop area depends on temperature and exhibits a turnover as a function of the strength of thermal noise--a phenomenon reminiscent of stochastic resonance. The numerical simulations agree well with our proposed analytical scheme.

Entropic dynamical hysteresis in a driven system.

We show that the application of a time periodic field driving a Brownian particle between the two lobes of a two-dimensional bilobal enclosure results in a hysteresis loop in the variation of integrated probability of residence of the particle as a function of the field. The confinement of the particle is characterized by symmetry breaking of the hysteresis loop, and the area of the loop exhibits a turnover with variation of frequency of the field. This dynamical hysteresis is geometry controlled, entropic in nature, and amenable to theoretical analysis with a two-state model.

Shape fluctuation-induced dynamic hysteresis.

We consider a system of Brownian particles confined in a two-dimensional bilobal enclosure whose walls are driven in time periodically by an external perturbation. The response of the particles under shape modulation is characterized by a relaxational delay which results in a non-vanishing area of the response function-field loop, response function being the integrated probability of residence of the particles in any of the lobes. This phenomenon is an entropic analogue of dynamical hysteresis, which vanishes in the quasi-static limit. The hysteresis loop area depends on temperature, strength of modulating field, and the geometrical parameters of the enclosure and exhibits a turnover as a function of frequency of the field.

Entropic noise-induced nonequilibrium transition.

We consider a system of Brownian particles confined in a two-dimensional bilobal enclosure. Varying cross-section of the confinement results in an effective entropic potential in reduced dimension. We show that the system may undergo an entropic noise-induced transition when the shape of the stationary probability density changes qualitatively from bimodal to trimodal type under the influence of a multiplicative noise.

Entropic resonant activation.

Varying cross section of confinement of a Brownian particle in two or higher dimensions results in an effective entropic barrier in reduced dimension. When the boundaries are subjected to periodic modulation, it is possible to observe a resonance of the mean first passage time between the lobes of a bilobal confined system as a function of the modulating frequency of the walls of the enclosure. The entropic resonant activation and the associated features, which are characteristic of the shape and size of the confinement, are amenable to a theoretical analysis in terms of a two-state model.