Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a “thermodynamic” theory can also be developed based on Tsallis’ generalized entropy S^(q)=∑_i=1^N(p_i-p_i^q)/[q(q-1)] and Shiino’s generalized free energy F^(q)=[∑_i=1^Np_i(p_i/π_i)^q-1-1]/[q(q-1)], where π_i is the stationary distribution. dF^(q)/dt=-f_d^(q)≤0 and it is zero if and only if the system is in its stationary state. dS^(q)/dt-Q_ex^(q)=f_d^(q), where Q_ex^(q) characterizes the heat exchange. For systems approaching equilibrium with detailed balance, f_d^(q) is the product of Onsager’s thermodynamic flux and force. However, it is discovered that the Onsager’s force is nonlocal. This is a consequence of the particular transformation invariance for zero energy of Tsallis’ statistics.The three-dimensional dynamics of a single non-Brownian flexible fiber in shear flow is evaluated numerically, in the absence of inertia. A wide range of ratios A of bending to hydrodynamic forces and hundreds of initial configurations are considered. We demonstrate that flexible fibers in shear flow exhibit much more complicated evolution patterns than in the case of extensional flow, where transitions to higher-order modes of characteristic shapes are observed when A exceeds consecutive threshold values. In shear flow, we identify the existence of an attracting steady configuration and different attracting periodic motions that are approached by long-lasting rolling, tumbling, and meandering dynamical modes, respectively. We demonstrate that the final stages of the rolling and tumbling modes are effective Jeffery orbits, with the constant parameter C replaced by an exponential function that either decays or increases in time, respectively, corresponding to a systematic drift of the trajectories. In the limit of C→0, the fiber aligns with the vorticity direction and in the limit of C→∞, the fiber periodically tumbles within the shear plane. AZD1390 mw For moderate values of A, a three-dimensional meandering periodic motion exists, which corresponds to intermediate values of C. Transient, close to periodic oscillations are also detected in the early stages of the modes.To mitigate errors induced by the cell’s heterogeneous noisy environment, its main information channels and production networks utilize the kinetic proofreading (KPR) mechanism. Here, we examine two extensively studied KPR circuits, DNA replication by the T7 DNA polymerase and translation by the E. coli ribosome. Using experimental data, we analyze the performance of these two vital systems in light of the fundamental bounds set by the recently discovered thermodynamic uncertainty relation (TUR), which places an inherent trade-off between the precision of a desirable output and the amount of energy dissipation required. We show that the DNA polymerase operates close to the TUR lower bound, while the ribosome operates ∼5 times farther from this bound. This difference originates from the enhanced binding discrimination of the polymerase which allows it to operate effectively as a reduced reaction cycle prioritizing correct product formation. We show that approaching this limit also decouples the thermodynamic uncertainty factor from speed and error, thereby relaxing the accuracy-speed trade-off of the system. Altogether, our results show that operating near this reduced cycle limit not only minimizes thermodynamic uncertainty, but also results in global performance enhancement of KPR circuits.We propose a method for enumerating entanglements between long chained, linear polymers that is based on the Gaussian linking number. The linking number is calculated between closely approaching segments of the macromolecular chains. Topological features of an entanglement, i.e., the extent to which one open segment winds around another, are reflected by the linking number. We show that using this measure, we can track disentanglement events through a deformation history and gain insights into how large scale disentanglements lead to failure. Incorporating an additional step where the topological entanglements identified along each chain are optimally clustered using standard clustering algorithms, we can also obtain a measure of the average number of rheological constraints that exist along each chain in an ensemble. Comparisons with other methods of enumerating entanglements, especially the primitive path analysis, are also made. Our results indicate that the linking number between two entangled segments in the undeformed state is a good indicator of the strength of the entanglement. Also, disentanglements occurring overwhelmingly around chain ends are an important cause of failure when a triaxial stress state exists in the polymer.Recent experiments show universal features of ratchet gear dynamics that are powered by different types of active baths. We investigate further for the case of a ratchet gear in a bath of self-propelling granular rods (SPRs). The resulting angular velocity was found to follow a nonmonotonic dependence to the SPR concentration similar to the observation from other active bath systems. This behavior is caused by the interplay of the momentum transfer of the SPRs in the trapping regions of the gear and the mean velocity of the SPRs inside the bath. For all SPR concentrations, we found that the angular velocity is proportional to the product of the number of SPRs pushing the gear and the SPRs mean velocity.We investigate the impact of attractive-repulsive interaction in networks of limit cycle oscillators. Mainly we focus on the design principle for generating an antiphase state between adjacent nodes in a complex network. We establish that a partial negative control throughout the branches of a spanning tree inside the positively coupled limit cycle oscillators works efficiently well in comparison with randomly chosen negative links to establish zero frustration (antiphase synchronization) in bipartite graphs. Based on the emergence of zero frustration, we develop a universal 0-π rule to understand the antiphase synchronization in a bipartite graph. Further, this rule is used to construct a nonbipartite graph for a given nonzero frustrated value. We finally show the generality of 0-π rule by implementing it in arbitrary undirected nonbipartite graphs of attractive-repulsively coupled limit cycle oscillators and successfully calculate the nonzero frustration value, which matches with numerical data. The validation of the rule is checked through the bifurcation analysis of small networks.