Search Results (4)

Traditional brain emulation approaches often rely on classical computational models that inadequately capture the stochastic, nonlinear, and potentially coherent features of biological neural systems. In this position paper, we introduce NeuroQ a quantum-inspired framework grounded in stochastic mechanics, particularly Nelson’s formulation. By reformulating the FitzHugh–Nagumo neuron model with structured noise, we derive a Schrödinger-like equation that encodes membrane dynamics in a quantum-like formalism. This formulation enables the use of quantum simulation strategies—including Hamiltonian encoding, variational eigensolvers, and continuous-variable models—for neural emulation. We outline a conceptual roadmap for implementing NeuroQ on near-term quantum platforms and discuss its broader implications for neuromorphic quantum hardware, artificial consciousness, and time-symmetric cognitive architectures. Rather than demonstrating a working prototype, this work aims to establish a coherent theoretical foundation for future research in quantum brain emulation. Full article

The review provides a pedagogical but comprehensive introduction to the foundations of a recently proposed statistical mechanics ($\mu$NEQT) of a stable nonequilibrium thermodynamic body, which may be either isolated or interacting. It is an extension of the well-established equilibrium statistical mechanics by considering microstates $\left\{{\mathfrak{m}}_k\right\}$ in an extended state space in which macrostates (obtained by ensemble averaging $\widehat{A}$) are uniquely specified so they share many properties of stable equilibrium macrostates. The extension requires an appropriate extended state space, three distinct infinitessimals $d_{\alpha }=(d,d_{\mathrm{e}},d_{\mathrm{i}})$ operating on various quantities q during a process, and the concept of reduction. The mechanical process quantities (no stochasticity) like macrowork are given by $\widehat{A}{d}_{\alpha }\mathsf{q}$, but the stochastic quantities ${\widehat{C}}_{\alpha }\mathsf{q}$ like macroheat emerge from the commutator ${\widehat{C}}_{\alpha }$ of $d_{\alpha }$ and $\widehat{A}$. Under the very common assumptions of quasi-additivity and quasi-independence, exchange microquantities $d_{\mathrm{e}}$q${}_k$ such as exchange microwork and microheat become nonfluctuating over $\left\{{\mathfrak{m}}_k\right\}$ as will be explained, a fact that does not seem to have been appreciated so far in diverse branches of modern statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.) that all use exchange quantities. In contrast, dq${}_k$ and $d_{\mathrm{i}}$q${}_k$ are always fluctuating. There is no analog of the first law for a microstate as the latter is a purely mechanical construct. The second law emerges as a consequence of the stability of the system, and cannot be violated unless stability is abandoned. There is also an important thermodynamic identity $d_{\mathrm{i}}Q\equiv d_{\mathrm{i}}W$$\ge 0$ with important physical implications as it generalizes the well-known result of Count Rumford and the Gouy-Stodola theorem of classical thermodynamics. The $\mu$NEQT has far-reaching consequences with new results, and presents a new understanding of thermodynamics even of an isolated system at the microstate level, which has been an unsolved problem. We end the review by applying it to three different problems of fundamental interest. Full article

We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations, which generate nonunitary transformation groups that we call instrumental Lie groups. The temporal evolution of the instrument is equivalent to the diffusion of a Kraus-operator distribution function, defined relative to the invariant measure of the instrumental Lie group. This diffusion can be analyzed using Wiener path integration, stochastic differential equations, or a Fokker-Planck-Kolmogorov equation. This way of considering instrument evolution we call the Instrument Manifold Program. We relate the Instrument Manifold Program to state-based stochastic master equations. We then explain how the Instrument Manifold Program can be used to describe instrument evolution in terms of a universal cover that we call the universal instrumental Lie group, which is independent not just of states, but also of Hilbert space. The universal instrument is generically infinite dimensional, in which case the instrument’s evolution is chaotic. Special simultaneous measurements have a finite-dimensional universal instrument, in which case the instrument is considered principal, and it can be analyzed within the differential geometry of the universal instrumental Lie group. Principal instruments belong at the foundation of quantum mechanics. We consider the three most fundamental examples: measurement of a single observable, position and momentum, and the three components of angular momentum. As these measurements are performed continuously, they converge to strong simultaneous measurements. For a single observable, this results in the standard decay of coherence between inequivalent irreducible representations. For the latter two cases, it leads to a collapse within each irreducible representation onto the classical or spherical phase space, with the phase space located at the boundary of these instrumental Lie groups. Full article

Among the famous formulations of quantum mechanics, the stochastic picture developed since the middle of the last century remains one of the less known ones. It is possible to describe quantum mechanical systems with kinetic equations of motion in configuration space based on conservative diffusion processes. This leads to the representation of physical observables through stochastic processes instead of self-adjoint operators. The mathematical foundations of this approach were laid by Edward Nelson in 1966. It allows a different perspective on quantum phenomena without necessarily using the wave-function. This article recaps the development of stochastic mechanics with a focus on variational and extremal principles. Furthermore, based on recent developments of optimal control theory, the derivation of generalized canonical equations of motion for quantum systems within the stochastic picture are discussed. These so-called quantum Hamilton equations add another layer to the different formalisms from classical mechanics that find their counterpart in quantum mechanics. Full article