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Small systems consisting of a few particles are increasingly technologically relevant. In such systems, an intense debate in microcanonical statistical mechanics has been about the correctness of Boltzmann’s surface entropy versus Gibbs’ volume entropy. While the former considers states within a fixed energy window centered around the energy of the system, the latter considers all states with energy lesser than or equal to the energy of the system. Both entropies have shortcomings─while Boltzmann entropy predicts unphysical negative/infinite absolute temperatures for small systems with an unbounded energy spectrum, Gibbs entropy entirely disallows negative absolute temperatures, in disagreement with experiments. We consider a relative energy window, motivated by the Heisenberg energy-time uncertainty principle and an eigenstate thermalization time inversely proportional to the system energy. The resulting entropy ensures positive, finite temperatures for systems without a maximum limit on their energy and allows negative absolute temperatures in bounded energy spectrum systems, e.g., with population inversion. It also closely matches canonical ensemble predictions for prototypical systems, for instance, correctly describing the zero-point energy of an isolated quantum harmonic oscillator. Overall, we enable accurate thermodynamic models for isolated systems with few degrees of freedom.

We study the dynamics of an athermal inertial active particle moving in a shear-thinning medium in $d=1$. The viscosity of the medium is modeled using a Coulomb-tanh function, while the activity is represented by an asymmetric dichotomous noise with strengths $-\Delta$ and $\mu\Delta$, transitioning between these states at a rate $\lambda$. Starting from the Fokker-Planck~(FP) equation for the time-dependent probability distributions $P(v,-\Delta,t)$ and $P(v,\mu\Delta,t)$ of the particle's velocity $v$ at time $t$, moving under the influence of active forces $-\Delta$ and $\mu\Delta$ respectively, we analytically derive the steady-state velocity distribution function $P_s(v)$, explicitly dependent on $\mu$. Also, we obtain a quadrature expression for the effective diffusion coefficient $D_e$ for the symmetric active force case~($\mu=1$). For a given $\Delta$ and $\mu$, we show that $P_s(v)$ exhibits multiple transitions as $\lambda$ is varied. Subsequently, we numerically compute $P_s(v)$, the mean-squared velocity $\langle v^2\rangle(t)$, and the diffusion coefficient $D_e$ by solving the particle's equation of motion, all of which show excellent agreement with the analytical results in the steady-state. Finally, we examine the universal nature of the transitions in $P_s(v)$ by considering an alternative functional form of medium's viscosity that also capture the shear-thinning behavior.

Hard-core lattice-gas models serve as minimal yet powerful models to explore entropy-driven phase transitions. In these models, particles are restricted from occupying neighboring sites up to a specified kth next-nearest neighbor, effectively bridging the behavior from simple nearest-neighbor exclusion to the continuum hard-sphere gas. While most prior studies have examined cases up to k = 3, this talk presents a detailed investigation of the lattice-gas model on a triangular lattice up to k = 7, using a rejection free flat histogram algorithm enhanced with cluster moves. Our findings reveal that for k = 3 to k = 7, the system exhibits a single, discontinuous phase transition from a low-density disordered fluid to a high-density sublattice-ordered phase. This conclusion is supported by the analysis of partition function zeros and the nonconvexity of entropy.

The basal ganglia are known to influence action selection and modulation of movement vigor, but whether and how they contribute to specifying the kinematics of learned motor skills is not understood. Here, we probe this question by recording and manipulating basal ganglia activity in rats trained to generate complex task-specific movement patterns with rich kinematic structure. We find that the sensorimotor arm of the basal ganglia circuit is crucial for generating the detailed movement patterns underlying the acquired motor skills. Furthermore, the neural representations in the striatum, and the control function they subserve, do not depend on inputs from the motor cortex. Taken together, these results extend our understanding of the basal ganglia by showing that they can specify and control the fine-grained details of learned motor skills through their interactions with lower-level motor circuits.

We uncover activity-driven crossover from phase separation to a new turbulent state in a two- dimensional system of counter-rotating spinners. We study the statistical properties of this active- rotor turbulence using the active-rotor Cahn-Hilliard-Navier-Stokes model, and show that the vor- ticity ω ∝ ϕ, the scalar field that distinguishes regions with different rotating states. We explain this intriguing proportionality theoretically, and we characterize power-law energy and concentra- tion spectra, intermittency, and flow-topology statistics. We suggest biological implications of such turbulence. This work has been done with Biswajit Maji and Nadia Bihari Padhan. https://arxiv.org/abs/2503.03843

Flying insects must balance the demands of speed and agility with the precision of their movements to swiftly and accurately respond to environmental stimuli. Achieving this balance requires them to integrate sensory information from various modalities. Of particular importance are visual inputs from their compound eyes and mechanosensory inputs from their antennae, which are crucial for maintaining flight stability. This challenge is particularly pronounced in insects like hawkmoths, which navigate under low light conditions. Prior studies on diverse hawkmoths and other insects have highlighted the critical role of antennal mechanosensory feedback in flight control, akin to the function of halteres in flies. How is such multisensory integration achieved? We addressed this question by conducting recordings from descending neurons in the cervical connective nerve in the Oleander hawkmoths, Daphnis nerii. The moths were provided with visual stimuli comprised of moving spots of light and mechanical stimuli to their antennae. While these stimuli were presented singly or concurrently, we recorded intracellularly from axons of descending interneurons to determine if they respond to one or both stimuli. In addition to a number of exclusively visual or mechanosensory descending neurons, we also identified several neurons that multiplex the visual and mechanosensory signals such that a single neuron encodes both visual stimuli from the compound eyes, and mechanosensory stimuli from the antennal Johnston's organs. Additional experiments at the level of behavior in intact moths reveals that integration of visual and antennal mechanosensory feedback plays a key role in gaze stabilization in flying hawkmoths. Together, these experiments underscore the importance of multisensory integration during flight in hawkmoths.

ynchronization of rhythmic units is essential for various biological functions. The synchronization mechanism is often governed by neural networks. For example, the circadian rhythm in mammals functions by synchronizing the gene expression rhythms of individual neurons within a neural tissue called the suprachiasmatic nucleus. Various movement patterns observed in animal locomotion, such as walking and swimming, are generated by neural networks known as central pattern generators. The synchronization dynamics of oscillator groups strongly depend on the heterogeneity of intrinsic frequencies, noise intensity, and the interaction network. If these factors can be estimated from observations, it can aid in understanding, predicting, and controlling the system, and contribute to elucidating the design principles of robust systems. However, estimation involves many challenges. Among them, estimation becomes exponentially difficult as the model's dimensions and the number of parameters increase. Therefore, it is desirable to assume a model with as low dimensions and as few parameters as possible. In the synchronization phenomena of oscillator groups, the phase oscillator model is expected to be useful. This presentation introduces research on estimation using the phase oscillator model [1,2]. [1]A Matsuki, H Kori, R Kobayashi: Network inference from oscillatory signals based on circle map, arXiv:2407.07445 (2024) [2]F Mori, H Kori: Noninvasive inference methods for interaction and noise intensities of coupled oscillators using only spike time data, Proceedings of the National Academy of Sciences 119, e2113620119 (2022)