Related papers: Functorial Statistical Physics: Feynman--Kac Formu…
Based on the covariant underdamped and overdamped Langevin equations with Stratonovich coupling to multiplicative noises and the associated Fokker-Planck equations on Riemannian manifold, we present the first law of stochastic…
In part I, using the theory of $\infty$-categories, we constructed a natural ``continuous action'' of $\operatorname {Ham} (M, \omega) $ on the Fukaya category of a closed monotone symplectic manifold. Here we show that this action is…
Statistical quantifiers are generically required to contract under physical evolutions, following the intuition that information should be lost under noisy transformations. This principle is very relevant in statistics, and it even allows…
We obtain an exact analytic expression for the dynamical structure factor of one-dimensional quantum gas of hard rods. Our result is valid for arbitrary many-body state of the system, with finite temperature states and the ground state…
We present quantum stochastic calculus in terms of diagrams taking weights in the algebra of observables of some quantum system. In particular, we note the absence of non-time-consecutive Goldstien diagrams. We review recent results in…
Each rule $f$ that assigns a vector $f(G)$ to an $(n+1)$-graph $G$ determines a class (or property) of $n$-manifold invariants. An invariant $v=v(M)$ is in this class if, for any triangulated manifold $|G|=M$, one has that $v(M)$ is a…
Stochastic processes play a key role for modeling a huge variety of transport problems out of equilibrium, with manifold applications throughout the natural and social sciences. To formulate models of stochastic dynamics the conventional…
Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle,…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
In this paper, we provide an integral equation characterization of the solution to a Cauchy problem associated to the Feynman-Kac formula for a regime-switching diffusion. We give a sufficient condition to guarantee the uniqueness of…
Starting from an axiomatic perspective, \emph{fluctuation geometry} is developed as a counterpart approach of inference geometry. This approach is inspired on the existence of a notable analogy between the general theorems of…
We consider the discrete time unitary dynamics given by a quantum walk on $\Z^d$ performed by a particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes…
For a stochastic system, its evolution from one state to another can have a large number of possible paths. Non-uniformity in the field of system variables leads the local dynamics in state transition varies considerably from path to path…
Fractional kinetic theory plays a vital role in describing anomalous diffusion in terms of complex dynamics generating semi-Markovian processes. Recently, the variational principle and associated Levy Ansatz have been proposed in order to…
In 1905, Einstein's theory of Brownian motion supported the molecular basis of the diffusion equation and introduced two complementary viewpoints: a deterministic field description and a probabilistic formulation based on stochastic…
The quantum fluctuations of a physical property can be observed in the measurement statistics of any measurement that is at least partially sensitive to that physical property. Quantum theory indicates that the effective distribution of…
We construct $C^\ast$-categories that are anologues of the categories used in controlled algebraic $K$-theory. We then show that the reduced $C^\ast$-algebra of a finitely presented group and an associated controlled $C^\ast$-category have…
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…
In this paper, we study intermittency properties for various stochastic PDEs with varieties of space time Gaussian noises via matching upper and lower moment bounds of the solution. Due to the absence of the powerful Feynman Kac formula,…
Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…