Introduction to Phase Transitions in Random Optimization Problems

We address the general problem of formulating the dynamical large deviations of non-Markovian systems in a closed form. Specifically, we consider a broad class of ``self-interacting'' jump processes whose dynamics depends on the past through a functional of a state-dependent empirical observable. Exploiting a natural separation of timescales, \newnewtext{and under the corresponding mixing conditions,} we obtain the exact (so-called ``level 2.5'') large deviation joint statistics of the empirical measure over configurations and of the empirical flux of transitions. As an application of this general framework, we derive explicit general bounds on the fluctuations of trajectory observables, generalising to the non-Markovian case both thermodynamic and kinetic uncertainty relations. We illustrate our theory with simple examples, and discuss potential applications of these results.

cond-mat.stat-mech↗

arXiv2026

Finite-time Polytropic Steering Reveals Non-monotonic Irreversibility

How irreversibility evolves from slow to fast driving is a central question in nonequilibrium thermodynamics. While near-equilibrium theory predicts increasing irreversibility with driving speed, the corresponding crossover far from equilibrium is not generally resolved within a unified control framework. Here we introduce polytropic steering, in which a prescribed relation between the ensemble energy and a time-dependent control parameter continuously organizes finite-time processes between isothermal and adiabatic limits. A Fokker-Planck formulation makes the construction applicable to general confining potentials, and yields closed-form thermodynamic expressions for a harmonic trap. We find a non-monotonic irreversibility: the entropy generation decreases in both the quasistatic and fast-driving limits and exhibits a maximum at an intermediate protocol duration. The resulting most-irreversible timescale quantifies the competition between thermal relaxation and external driving. We verify the persistence of this behavior in an anharmonic optical-lattice potential and demonstrate how the same steering principle controls power-efficiency trade-offs in finite-time Brownian engines.

cond-mat.stat-mech↗

arXiv2026

Enhanced synchronization with proportional coupling in Kuramoto oscillator networks under a fixed coupling budget

We propose an explicit coupling scheme for enhancing the synchronization of Kuramoto oscillator networks under a fixed coupling budget. We show that by scaling the interaction strength between oscillators according to their frequency detuning, synchronization is enhanced. The coupling scheme produces a crossover from a smooth Kuramoto onset to an abrupt, hysteretic synchronization transition as a single allocation parameter is varied. Our work offers a general route to efficient synchronization in engineered Kuramoto networks and provides insight into their critical behavior.

cond-mat.stat-mech↗