scholarly journals Comparing Wigner, Husimi and Bohmian distributions: which one is a true probability distribution in phase space?

2015 ◽  
Vol 14 (4) ◽  
pp. 894-906 ◽  
Author(s):  
E. Colomés ◽  
Z. Zhan ◽  
X. Oriols
Keyword(s):  
Phase Space ◽  
Probability Distribution ◽  
True Probability

Thermodynamic non-additivity in disordered systems with extended phase space

Open Physics ◽  
2004 ◽  
Vol 2 (2) ◽  
Author(s):  
Eduard Vakarin ◽  
Jean Badiali
Keyword(s):  
Phase Space ◽  
Probability Distribution ◽  
Disordered Systems ◽  
Stochastic Systems ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Thermodynamic Entropy ◽  
Dynamic Stochastic ◽  
Replica Approach ◽  
Dynamic Subsystem

AbstractNon-additivity effects in coupled dynamic-stochastic systems are investigated. It is shown that there is a mapping of the replica approach to disordered systems with finite replica indexn on Tsallis non-extensive statistics, if the average thermodynamic entropy of the dynamic subsystem differs from the information entropy for the probability distribution in the stochastic subsystem. The entropic indexq is determined by the entropy difference ΔS. In the case of incomplete information, the entropic indexq=1−n is shown to be related to the degree of lost information.

Application of the Phase Space Quasi-Probability Distribution to the Nuclear Shell Model

1960 ◽  
Vol 120 (1) ◽  
pp. 254-264 ◽  
Author(s):  
George A. Baker ◽  
Ian E. McCarthy ◽  
Charles E. Porter
Keyword(s):  
Phase Space ◽  
Probability Distribution ◽  
Shell Model ◽  
Nuclear Shell Model ◽  
Nuclear Shell

Choice under Limited Uncertainty

2006 ◽  
Vol 6 (1) ◽  
Author(s):  
Ettore Damiano
Keyword(s):  
Probability Distribution ◽  
Expected Utility ◽  
Selection Rule ◽  
Subjective Expected Utility ◽  
Subjective Probabilities ◽  
True Probability ◽  
Utility Maximizer ◽  
The Third ◽  
Choice Under Uncertainty ◽  
New Framework

This paper considers the problem of an agent's choice under uncertainty in a new framework. The agent does not know the true probability distribution over the state space but is objectively informed that it belongs to a specified set of probabilities. Maintaining the hypothesis that this agent is a subjective expected utility maximizer, we address the question of how the objective information influences her subjective prior.Three plausible rules are proposed. The first, named state independence, states that the subjective probability should not depend on how the uncertain states are `labeled'. Location-consistency, the second property, assumes that `similar' objective sets of probabilities result in `similar' subjective priors. The third rule is an `update-consistency' rule. Suppose the agent selects some probability p. She is then told that the likelihood assigned by p to some event A is in fact correct; then this should not cause her to revise her choice of p.Another property, alternative to update-consistency, is also proposed. When an agent forms her subjective prior assigning subjective probabilities to events in some ordered sequence, this property requires that the resulting prior be independent of that order. This last property, named order independence, is shown to be equivalent to update-consistency.A class of sets of probabilities is found on which state independence, location-consistency and update consistency (order independence) uniquely determine a selection rule. Some intuition is given regarding why these properties work in this collection of problems.

scholarly journals Classical thermodynamics from quasi-probabilities

2016 ◽  
Vol 30 (03) ◽  
pp. 1650005
Author(s):  
F. Pennini ◽  
A. Plastino ◽  
M. C. Rocca
Keyword(s):  
Phase Space ◽  
Probability Distribution ◽  
Effective Temperature ◽  
Probability Distributions ◽  
Thermodynamic Description ◽  
Important Case ◽  
Quadratic Hamiltonians ◽  
Classical Thermodynamics ◽  
Unified Description

The basic idea of a microscopic understanding of thermodynamics is to derive its main features from a microscopic probability distribution. In such a vein, we investigate the thermal statistics of quasi-probabilities’s semiclassical analogs in phase space for the important case of quadratic Hamiltonians, focusing attention in the three more important instances, i.e. those of Wigner, [Formula: see text]- and Husimi distributions. Introduction of an effective temperature permits one to obtain a unified thermodynamic description that encompasses and unifies the three different quasi-probability distributions. This unified description turns out to be classical.

Distributionally Robust Stochastic Model Predictive Control for Collision Avoidance

2019 ◽  
Author(s):  
Baisravan HomChaudhuri
Keyword(s):  
Probability Distribution ◽  
Collision Avoidance ◽  
Controller Design ◽  
Probability Distributions ◽  
Optimization Methods ◽  
Linear Matrix ◽  
True Probability ◽  
Exact Probability ◽  
Exact Probability Distribution ◽  
Distributionally Robust

Abstract This paper focuses on distributionally robust controller design for avoiding dynamic and stochastic obstacles whose exact probability distribution is unknown. The true probability distribution of the disturbance associated with an obstacle, although unknown, is considered to belong to an ambiguity set that includes all the probability distributions that share the same first two moment. The controller thus focuses on ensuring the satisfaction of the probabilistic collision avoidance constraints for all probability distributions in the ambiguity set, hence making the solution robust to the true probability distribution of the stochastic obstacles. Techniques from robust optimization methods are used to model the distributionally robust probabilistic or chance constraints as a semi-definite programming (SDP) problem with linear matrix inequality (LMI) constraints that can be solved in a computationally tractable fashion. Simulation results for a robot obstacle avoidance problem shows the efficacy of our method.

scholarly journals Approaching probabilistic and deterministic nomic truths in an inductive probabilistic way

Synthese ◽  
2021 ◽  
Author(s):  
Theo A. F. Kuipers
Keyword(s):  
Probability Distribution ◽  
Prior Distribution ◽  
Multinomial Distribution ◽  
Truth Approximation ◽  
True Probability ◽  
Theories Of Truth ◽  
Inductive Probability ◽  
Probability Field ◽  
Probabilistic Approximation ◽  
Probabilistic Context

AbstractTheories of truth approximation in terms of truthlikeness (or verisimilitude) almost always deal with (non-probabilistically) approaching deterministic truths, either actual or nomic. This paper deals first with approaching a probabilistic nomic truth, viz. a true probability distribution. It assumes a multinomial probabilistic context, hence with a lawlike true, but usually unknown, probability distribution. We will first show that this true multinomial distribution can be approached by Carnapian inductive probabilities. Next we will deal with the corresponding deterministic nomic truth, that is, the set of conceptually possible outcomes with a positive true probability. We will introduce Hintikkian inductive probabilities, based on a prior distribution over the relevant deterministic nomic theories and on conditional Carnapian inductive probabilities, and first show that they enable again probabilistic approximation of the true distribution. Finally, we will show, in terms of a kind of success theorem, based on Niiniluoto’s estimated distance from the truth, in what sense Hintikkian inductive probabilities enable the probabilistic approximation of the relevant deterministic nomic truth. In sum, the (realist) truth approximation perspective on Carnapian and Hintikkian inductive probabilities leads to the unification of the inductive probability field and the field of truth approximation.

scholarly journals Mortality rate and estimate of fraction of undiagnosed COVID-19 cases in the US in March and April 2020

2020 ◽  
Author(s):  
RuShan Gao ◽  
Karen H. Rosenlof
Keyword(s):  
Simple Model ◽  
Probability Distribution ◽  
Total Mortality ◽  
True Probability ◽  
Probability Curve ◽  
Mortality Probability ◽  
Death Probability ◽  
The Us ◽  
Peak Location

We use a simple model to derive a mortality probability distribution for a patient as a function of days since diagnosis (considering diagnoses made between 25 February and 29 March 2020). The peak of the mortality probability is the 13th day after diagnosis. The overall shape and peak location of this probability curve are similar to the onset-to-death probability distribution in a case study using Chinese data. The total mortality probability of a COVID-19 patient in the US diagnosed between 25 February and 29 March is about 21%. We speculate that this high value is caused by severe under-testing of the population to identify all COVID-19 patients. With this probability, and an assumption that the true probability is 2.4%, we estimate that 89% of all SARS-CoV-2 infection cases were not diagnosed during this period. When the same method is applied to data extended to 25 April, we found that the total mortality probability of a patient diagnosed in the US after 1 April is about 6.4%, significantly lower than for the earlier period. We attribute this drop to increasingly available tests. Given the assumption that the true mortality probability is 2.4%, we estimate that 63% of all SARS-CoV-2 infection cases were not diagnosed during this period (1 - 25 April).

TWO-MODE PHASE-STATE REPRESENTATIONS IN QUANTUM OPTICS

2001 ◽  
Vol 15 (25) ◽  
pp. 1155-1169
Author(s):  
HONG-YI FAN ◽  
XIAN-TING LIANG ◽  
ZHI-HU SUN
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Probability Distribution ◽  
Quantum Optics ◽  
Probability Distribution Function ◽  
Light Field ◽  
Phase State ◽  
Light Fields ◽  
Space Formalism ◽  
Phase Probability Distribution

A phase state presentation |ξ= reiθ> for a two-mode light field is constructed in the context of quantum optics. This phase space formalism is directly connected to phase-related operators. The generalized quasi-probability distribution function Q(ξ) and measurable phase probability distribution function P(θ) are constructed and are useful to obtain information about phase properties of light fields.

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