Statistical Mechanics
This paper introduces a novel approach to financial crisis prediction by establishing a thermodynamic-like framework derived from the fluctuation theorem of statistical physics. We define market temperature through the probability ratio of…
We study symmetric L\'evy flights in a semi-infinite domain $[0,\infty)$ with a reflecting and absorbing boundary at 0. To this end, we use the fractional differential equation that governs the L\'evy process. Incorporating the boundary…
What are the fundamental limitations placed by the laws of thermodynamics on the energy expenditure needed to carry out a given task in a nonequilibrium environment in finite time? In this thesis, we investigate "optimal nonequilibrium…
We present a detailed study of the finite-size one-dimensional quantum XY chain in a transverse field in the presence of boundary fields coupled with the order-parameter spin operator. We consider fields located at the chain boundaries that…
The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Ising model and construct percolation clusters by placing bonds,…
It is well-known that evaporation can lead to cooling. However, little is known that evaporation can actually create a refrigeration effect, i.e., the vapor phase temperature can drop below the temperature of the cooling wall. This…
Characterising the statistical properties of classical interacting particle systems is a long-standing question. For Brownian particles the microscopic density obeys a stochastic evolution equation, known as the Dean--Kawasaki equation.…
It is a central problem in various fields of physics to elucidate the behavior of quantum many-body systems subjected to bulk dissipation. In this context, several microscopic derivations of the Lindblad quantum master equation for…
We consider a discrete-time continuous-space random walk, with a symmetric jump distribution, under stochastic resetting. Associated with the random walker are cost functions for jumps and resets, and we calculate the distribution of the…
The dynamics of numerous physical systems, such as spins and qubits, can be described as a series of rotation operations, i.e., walks in the manifold of the rotation group. A basic question with practical applications is how likely and…
Fluctuations exist in any material object $A$. If $A$ has non-zero temperature $T$, one speaks about thermal fluctuations. If $A$ is at very low $T$, the fluctuations are of quantum origin. Interesting effects appear if two bodies $A$ and…
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…
We report a dynamical phase transition in the information spreading within a classical 2D deterministic interacting many-body system. Specifically, the transition is observed in a recently introduced momentum-conserving parity check…
Motivated by modelling in physics and other disciplines, such as sociology and psychology, we derive the mean field of the general-spin Ising model from the variational principle of the Gibbs free energy. The general-spin Ising model has…
We study the $J_1$-$J_2$ Ising model on the honeycomb lattice, considering ferromagnetic interactions between first neighbors ($J_1$) and antiferromagnetic interactions between second neighbors ($J_2$). Our analysis is based on the…
Nonreciprocal interactions are widely observed in nonequilibrium systems, from biological or sociological dynamics to open quantum systems. Despite the ubiquity of nonreciprocity, its impact on phase transitions is not fully understood. In…
We consider a model of interacting random walkers on a triangular chain and triangular lattice, where a particle can move only if the other two sites of the triangle are unoccupied -- a kinetically-constrained hopping process (KCHP)…
Dynamical quantum phase transitions (DQPTs) have been studied in the extended XY model under both noiseless and noisy linear driven staggered field cases. In the time-independent staggered field case, the model exhibits a single critical…
The one-dimensional (1D) $J_1$-$J_2$ $q$-state Potts model is solved exactly for arbitrary $q$ by analytically block-diagonalizing the original $q^2\times q^2$ transfer matrix into a simple $2\times 2$ maximally symmetric subspace, based on…
Quantifying and characterizing fluctuations far away from equilibrium is a challenging task. We discuss and experimentally confirm a series expansion for a driven classical system, relating the different non-equilibrium cumulants of the…