Related papers: Work distribution and path integrals in general me…
The asymptotic behaviour of the work probability distribution in driven non-equilibrium systems is determined using the method of optimal fluctuations. For systems described by Langevin dynamics the corresponding Euler-Lagrange equation…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a…
We study the response of generating functionals to a variation of parameters (couplings) in equilibrium systems i.e. in quantum field theory (QFT) and equilibrium statistical mechanics. These parameters can be either physical ones such as…
We illustrate the Jarzynski equality on the exactly solvable model of a one-dimensional ideal gas in uniform expansion or compression. The analytical results for the probability density $P(W)$ of the work $W$ performed by the gas are…
Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…
Recent studies of in vitro evolution of DNA via protein binding indicate that the evolution behavior is qualitatively different in different parameter regimes. I here present a general theory that is valid for a wide range of parameters,…
We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a…
The fluctuation theorems, and in particular, the Jarzynski equality, are the most important pillars of modern non-equilibrium statistical mechanics. We extend the quantum Jarzynski equality together with the Two-Time Measurement Formalism…
Based on the relationship that the interaction energy between any two subsystems is equal to their internal energy multiplied by the interaction coefficient, we have derived a series correlated expressions of statistical physical…
Thermodynamics constrains changes to the energy of a system, both deliberate and random, via its first and second laws. When the system is not in equilibrium, fluctuation theorems such as the Jarzynski equality further restrict the…
We give a quantum version of the Jarzynski relation between the distribution of work done over a certain time-interval on a system and the difference of equilibrium free energies. The main new ingredient is the identification of work…
We consider a model of cultural evolution for a strategy selection in a population of individuals who interact in a game theoretic framework. The evolution combines individual learning of the environment (population strategy profile),…
Many studies of quantum-size heat engines assume that the dynamics of an internal system is unitary and that the extracted work is equal to the energy loss of the internal system. Both assumptions, however, should be under scrutiny. In the…
A path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase…
The theory of phenomenological Non-equilibrium Thermodynamics is extended by includimg stochastic processes in order to account for recently derived thermodynamical relations such as the Jarzynski equality. Four phenomenological axioms are…
Dynamical systems driven by strong external signals are ubiquituous in nature and engineering. Here we study "echo state networks", networks of a large number of randomly connected nodes, which represent a simple model of a neural network,…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
This work tackles the problem of energy-efficient distributed power control in wireless networks with a large number of transmitters. The problem is modeled by a dynamic game. Each transmitter-receiver communication is characterized by a…
We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck…