Related papers: Generalized pathway entropy and its applications i…
A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential…
Following the work on Shannon entropy together with the principle of maximum entropy, Luo & Singh (J. Hydrol. Eng., 2011, 16(4): 303-315) and Singh & Luo (J. Hydrol. Eng., 2011, 16(9): 725-735) explored the concept of non-extensive Tsallis…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
A general principle called "conservation of the ellipsoid of concentration" is introduced and a generalized entropic form of order 'alpha' is optimized under this principle. It is shown that this can produce a density which can act as a…
The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…
Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter $\alpha$, called the pathway parameter, one can connect generalized type-1 beta family…
We generalize Einstein's probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected…
The growing interest of different entropy functions proposed so far (like the Bekenstein-Hawking, Tsallis, R\'{e}nyi, Barrow, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies) towards black hole thermodynamics as well as towards…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
In this thesis we start by providing some detail regarding how we arrived at our present understanding of probabilities and how we manipulate them - the product and addition rules by Cox. We also discuss the modern view of entropy and how…
The coincidence method of measuring the entropy of a system, proposed some time ago by Ma, is generalized to include systems out of equilibrium. It is suggested that the method can be adapted to analyze multiparticle states produced in…
This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…
Starting from an algebraic approach of quantum physics it has been shown via the Tomita-Takesaki theorem and the KMS condition that the canonical density matrix contains the dynamics of the system provided we use a rescaling of time. In…
We show that in the continuum limit, the average spectrum method (ASM) is equivalent to maximizing R\'enyi entropies of order $\eta$, of which Shannon entropy is the special case $\eta=1$. The order of R\'enyi entropy is determined by the…
The design space of discrete-space diffusion or flow generative models are significantly less well-understood than their continuous-space counterparts, with many works focusing only on a simple masked construction. In this work, we aim to…
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the…
Reaction-diffusion systems driven far from thermodynamic equilibrium through the injection of energy can support multiple distinct spatial patterns that persist as long-lived dynamical phases. The stability of these metastable phases is not…
Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An integration by parts formula is derived for the carr\'e du champ of a Markov process in an abstract space. It leads to a time reversal formula…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…