Related papers: Statistical System based on $p$-adic numbers
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase…
We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic…
Dynamical system properties give rise to effects in Statistical Mechanics. Topological index changes can be the basis for phase transitions. The Euler characteristic is a versatile topological invariant that can be evaluated for model…
Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, \textit{what is thermodynamics?}, has remained…
Many processes in nature seem to be entirely controlled by transition rates and the corresponding statistical dynamics. Some of them are in essence quantum, like the decay of excited states, the tunneling through barriers or the decay of…
I consider the generic situation where a finite number of identical test systems in varying (possibly unknown) initial states are subjected independently to the same unknown process. I show how one can infer from the output data alone…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
Thermodynamic conventions suffer from describing dynamical distinctions, especially when the structural and energetic changes induced by localized rare events are insignificant. By using the ensemble theory in the trajectory space, we…
In this book, we study Statistical Physics under conditions of thermodynamic equilibrium, starting from the definition of statistical ensembles. The book is divided into five chapters: First, a brief introduction to statistical methods.…
In open systems with strong coupling, the interaction energy between the system and the environment is significant, so thermodynamic quantities cannot be reliably obtained by traditional statistical mechanics methods. The Hamiltonian of…
In order to extend the recently proposed Monte Carlo Hamiltonian to many-body systems, we suggest to concept of a stochastic basis. We apply it to the chain of $N_s=9$ coupled anharmonic oscillators. We compute the spectrum of excited…
Thermodynamic quantities, like heat, entropy, or work, are random variables, in stochastic systems. Here, we investigate the statistics of the heat exchanged by a Brownian particle subjected to a logarithm-harmonic potential. We derive…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equivalently, statistical mechanical states, can be…
We provide a complete thermodynamic solution of a 1D hopping model in the presence of a random potential by obtaining the density of states. Since the partition function is related to the density of states by a Laplace transform, the…
It is shown that statistical mechanics is applicable to isolated quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, or quantum dots in solids, where the residual two-body interaction is sufficiently…
Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a…
We argue here that, as it happens in Classical and Quantum Mechanics, where it has been proven that alternative Hamiltonian descriptions can be compatible with a given set of equations of motion, the same holds true in the realm of…