arXiv subjects

Arnaldo Spalvieri

Publications and source records attributed to Arnaldo Spalvieri.

8 recordsLinked to original sources

arXiv2025

Energy Optimization for Time-of-Arrival Based Tracking

The paper analyzes energy allocation in a scenario where the position of a moving target is tracked by exploiting the Time-of-Arrivals of bandwidth-constrained signals received by or transmitted from a fixed number of anchors located at known positions. The signal of each anchor is generated by transmitting a sequence of known symbols, allowing for amplitude and duration (number of symbols) to be different from anchor to anchor. The problem is the minimization of the sum of the energies of the transmitted signals imposing a constraint on the performance of the tracking procedure. Specifically, the constraint is the Posterior Cramer-Rao Bound, below the mean square error achieved by any unbiased estimator. The main improvement over the previous literature is the derivation of a formula that, at each step of the tracking, allows to calculate in closed form the first-order variation of the Posterior Cramer-Rao Bound as a function of the variation of the total energy. To concretely show the application of our approach, we present also two numerical algorithms that implement the constrained optimization in the case of signals of fixed amplitude and variable duration transmitted from the anchors in a time division multiplexing scheme.

eess.SP↗

arXiv2025

Canonical Distribution of the Occupancy Numbers of Bosonic Systems

The paper works out the canonical probability distribution of the occupancy numbers of a bosonic system and shows that canonical typicality applies to the canonical density operator of the occupancy numbers. The result is that, if, as it is today standard, the canonical system's mixed state is obtained by tracing out the environment from any typical pure state of the universe, then asymptotically the canonical probability distribution of system's occupancy numbers tends in probability to the multinomial distribution. The paper also shows that the currently accepted probability distribution of the occupancy numbers of a system with fixed number of particles is not compatible with the commonly accepted notion of canonical system.

cond-mat.stat-mech↗

arXiv2025

Canonical Thermodynamics

The paper demonstrates that the canonical probability distribution of the occupancy numbers of a bosonic system is multinomial, and shows how the thermodynamics of the canonical system descends from this distribution. The categorical distribution (i.e. the one-particle probability distribution of occupancy of the quantum eigenstates allowed to a particle of the system) of the multinomial distribution should be derived from constrained maximization of the Shannon entropy of the multinomial distribution. However, since the multinomial distribution intractable, one must renounce to a closed-form solution to the constrained maximization problem. The analysis is then focused on the thermal state, that is characterized by the constraint on system's expected energy. In this case, the paper proposes to consider a suboptimal tractable categorical distribution, which is likely to be close to the actual categorical maximizer, and shows that the one-particle Boltzmann distribution is a good approximation to the actual categorical maximizer only in certain cases, including the classical regime. The unexpected result is that, in the general case, the approximation that we find to the categorical maximizer is not of exponential type, or, in other words, is not the one-particle Boltzmann distribution. As a consequence, the probability distribution of microstates is not of exponential type. As in the standard analysis, it is always equal to the product of factors but, in the general case, these factors are not the Boltzmann factors, therefore the probability of a microstate can be different from the probability of another microstate even when the two have the same energy.

cond-mat.stat-mech↗

arXiv2023

Entropy of the Canonical Occupancy (Macro) State in the Quantum Measurement Theory

The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is derived both by tracing out the environment from a bosonic eigenstate of the union of environment and system of interest (the empirical approach) and by tracing out the environment from the mixed state of the union of environment and system of interest (the Bayesian approach). In the thermodynamic limit, the two coincide and are equal to the multinomial distribution. Furthermore, the paper proposes to identify the physical entropy of the bosonic system with the Shannon entropy of the occupancy numbers, fixing certain contradictions that arise in the classical analysis of thermodynamic entropy. Finally, by leveraging an information-theoretic inequality between the entropy of the multinomial distribution and the entropy of the multivariate hypergeometric distribution, Bayesianism and empiricism are integrated into a common ''infomechanical'' framework.

quant-ph↗

arXiv2023

The Exact Entropy Formula of the Ideal Gas and its Information-Theoretic Interpretation

The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation is that, under this assumption, whichever is the number of particles that constitute the system, the occupancy numbers of system's quantum (micro)states are multinomially distributed. This observation leads to an entropy formula for the physical system, which is nothing else than the entropy formula of the multinomial distribution, for which we claim novelty, in the sense that it is proposed here for the first time that the entropy of the multinomial distribution is the entropy of the physical system. The entropy formula of the multinomial distribution unveils yet unexplored connections between information theory and statistical mechanics, among which we mention the connection between conditional entropy of the random microstate given the random occupancy numbers and the Boltzmann-Planck entropy $\log(W)$ and between these two and the Gibbs correction term $\log(N!)$, thermalization and communication-theoretic preparation of a thermal state, accessible information of the thermal state and physical entropy of the thermalized system. A noticeable specific result that descends from our approach is the exact quantum correction to the textbook Sackur-Tetrode formula for the entropy of an ideal gas at the thermal equilibrium in a container.

cond-mat.stat-mech↗

arXiv2023

Infomechanics of Independent and Identically Distributed Particles

The paper moves a step towards the full integration of statistical mechanics and information theory. Starting from the assumption that the thermodynamical system is composed by particles whose quantized energies can be modelled as independent and identically distributed random variables, the paper proposes an approach whose cornerstones are the information-theoretic typical set and the conditional equiprobability of microstates given certain macrostates of the system. When taken together, these two concepts explain why the standard assumption of equally probable microstates is non-necessary (if not misleading) and show that the celebrated Boltzmann-Planck entropy is indeed a conditional entropy with deterministic condition. Several new specific results of physical relevance are derived from this approach, among which are the probability distribution of the occupancy numbers of the energy levels and an exact formula for the ideal gas in a container that gives the entropy of the gas also at low temperature. These specific results are pieces of a self-consistent and unified framework that encompasses the cases of low and high temperature, of indexed and non-indexed particles, of small and large number of particles, of microcanonical, canonical and grand canonical ensembles.

cond-mat.stat-mech↗

arXiv2021

The Shannon-McMillan Theorem Proves Convergence to Equiprobability of Boltzmann's Microstates

The paper shows that, for large number of particles and for distinguishable and non-interacting identical particles, convergence to equiprobability of the $W$ microstates of the famous Boltzmann-Planck entropy formula $S=k \log(W)$ is proved by the Shannon-McMillan theorem, a cornerstone of information theory. This result further strengthens the link between information theory and statistical mechanics.

physics.class-ph↗

arXiv2013

Tight Upper and Lower Bounds to the Information Rate of the Phase Noise Channel

Numerical upper and lower bounds to the information rate transferred through the additive white Gaussian noise channel affected by discrete-time multiplicative autoregressive moving-average (ARMA) phase noise are proposed in the paper. The state space of the ARMA model being multidimensional, the problem cannot be approached by the conventional trellis-based methods that assume a first-order model for phase noise and quantization of the phase space, because the number of state of the trellis would be enormous. The proposed lower and upper bounds are based on particle filtering and Kalman filtering. Simulation results show that the upper and lower bounds are so close to each other that we can claim of having numerically computed the actual information rate of the multiplicative ARMA phase noise channel, at least in the cases studied in the paper. Moreover, the lower bound, which is virtually capacity-achieving, is obtained by demodulation of the incoming signal based on a Kalman filter aided by past data. Thus we can claim of having found the virtually optimal demodulator for the multiplicative phase noise channel, at least for the cases considered in the paper.

cs.IT↗