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We analyze a token-based Brownian circuit in which Brownian particles, coined `tokens,' move randomly by exploiting thermal fluctuations, searching for a path in multi-token state space corresponding to the solution of a given problem. The…
We study the emergence of anticoncentration and approximate unitary design behavior in local Brownian circuits. The dynamics of circuit averaged moments of the probability distribution and entropies of the output state can be represented as…
A graph-theoretic analysis of the steady-state current noise in master equations under a finite thermodynamic force (affinity) is presented. The incidence matrix twisted by a finite affinity is not orthogonal to the standard cycle space,…
Collisional Brownian engines have attracted significant attention due to their simplicity, experimental accessibility, and amenability to exact analytical solutions. While previous research has predominantly focused on optimizing mean…
Fluctuations are significant in mesoscopic systems and of particular importance in understanding quantum transport. Here, we show that fluctuations can be considered as a resource for the operations of open quantum systems as functional…
The energy cost of computation has emerged as a central challenge at the intersection of physics and computer science. Recent advances in statistical physics -- particularly in stochastic thermodynamics -- enable precise characterizations…
Brownian clocks are biomolecular networks that can count time. A paradigmatic example are proteins that go through a cycle thus regulating some oscillatory behaviour in a living system. Typically, such a cycle requires free energy often…
Brownian computers utilize thermal fluctuations as a resource for computation and hold promise for achieving ultra-low-energy computations. However, the lack of a statistical direction in Brownian motion necessitates the incorporation of…
We introduce a prime number generator in the form of a stochastic algorithm. The character of such algorithm gives rise to a continuous phase transition which distinguishes a phase where the algorithm is able to reduce the whole system of…
This paper is concerned with the stochastic thermodynamics of non-equilibrium Gaussian processes that can exhibit anomalous diffusion. In the systems considered, the noise correlation function is not necessarily related to friction. Thus,…
We analyze the thermodynamic cost of a logically reversible Brownian Turing machine operating in the first-passage time protocol based on the stochastic thermodynamics of resetting. In this framework, the thermodynamic cost of computation…
We consider a model of active Brownian particles with velocity-alignment in two spatial dimensions with passive and active fluctuations. Hereby, active fluctuations refers to purely non-equilibrium stochastic forces correlated with the…
We obtain the fluctuations for the occupation time of one-dimensional symmetric exclusion processes with speed change, where the transition rates (conductances) are driven by a general function W. The approach does not require sharp bounds…
In the last ten years, a number of ``Conventional Fluctuation Theorems'' have been derived for systems with deterministic or stochastic dynamics, in a transient or in a non-equilibrium stationary state. These theorems gave explicit…
Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…
In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite…
We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase…
In contrast to the classical concept of a Carnot engine that alternates contact between heat baths of different temperatures, naturally occurring processes usually harvest energy from anisotropy, being exposed simultaneously to chemical and…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
This article analyzes the behavior of a Brownian fluctuation process under a mixed strategic game setup. A variant of a compound Brownian motion has been newly proposed, which is called the Shifted Brownian Fluctuation Process to predict…