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Macroscopic Behaviour in a Two-Species Exclusion Process Via the Method of Matched Asymptotics
We consider a two-species simple exclusion process on a periodic lattice. We use the method of matched asymptotics to derive evolution equations for...
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Condensation of Non-reversible Zero-Range Processes
In this article, we investigate the condensation phenomena for a class of non-reversible zero-range processes on a fixed finite set. By establishing...
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Background
Stochastic thermodynamics is an extended form of thermodynamics to small fluctuating systems such as Brownian particles, molecular motors in living...
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Reconstruction of Stochastic Dynamical Equations: Exemplary Diffusion, Jump-Diffusion Processes and Lévy Noise-Driven Langevin Dynamics
In this chapter we reconstruct stochastic dynamical equations with known drift and diffusion coefficients, as well as known properties of jumps, jump...
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Metastability in a Stochastic System of Spiking Neurons with Leakage
We consider a finite system of interacting point processes with memory of variable length modeling a finite but large network of spiking neurons with...
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Quantum Markov processes: From attractor structure to explicit forms of asymptotic states
Markov processes play an important role in physics and in particular in the theory of open systems. In this paper we study the asymptotic evolution...
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Photon Frequency Diffusion Process
We introduce a stochastic multi-photon dynamics on reciprocal space. Assuming isotropy, we derive the diffusion limit for a tagged photon to be a...
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Thermodynamic Uncertainty Relation
The thermodynamic uncertainty relation, abbreviated as TUR, concerns a current fluctuation around the nonequilibrium steady state.
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Variational Aspects of Entropy Production
In Part II, we have seen several equalities on entropy production including the fluctuation theorem. In this Part, we have seen several inequalities...
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Nonequilibrium Statistical Physics
Although most many-body systems are beyond the technical possibilities of the mathematical calculus of mechanics, we are able to calculate the...
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Continuous-Time Random Walks and Temporal Networks
Real-world networks often exhibit complex temporal patterns that affect their dynamics and function. In this chapter, we focus on the mathematical...
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Information Thermodynamics
One important achievement of stochastic thermodynamics is a clarification of the role of information in thermodynamics, which is a longstanding...
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Contagion dynamics on higher-order networks
A paramount research challenge in network and complex systems science is to understand the dissemination of diseases, information and behaviour. The...
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Invariant Measure for Stochastic Schrödinger Equations
Quantum trajectories are Markov processes that describe the time evolution of a quantum system undergoing continuous indirect measurement....
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On the Telegraph Process Driven by Geometric Counting Process with Poisson-Based Resetting
We investigate the effects of the resetting mechanism to the origin for a random motion on the real line characterized by two alternating velocities
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How to Set Up Stochastic Equations for Real World Processes: Markov–Einstein Time Scale
In Chaps. 16 – 21 we address a central question in...
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Speed Limit for State Transformation
In the research of speed limit inequalities, we investigate what is the cost of quick state transformations.
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Monte Carlo Simulations in Quantum Mechanics
This chapter provides an introduction to particular Markov processes which obey the detailed balance condition. We explain the Metropolis...