Related papers: Physics of the Shannon Limits
Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper…
Connections between information theory and thermodynamics have proven to be very useful to establish bounding limits for physical processes. Ideas such as Landauer's erasure principle and information assisted work extraction have greatly…
We argue that the entanglement entropy for a very small subsystem obeys a property which is analogous to the first law of thermodynamics when we excite the system. In relativistic setups, its effective temperature is proportional to the…
According to E.T. Jaynes and E.P. Wigner, entropy is an anthropomorphic concept in the sense that in a physical system correspond many thermodynamic systems. The physical system can be examined from many points of view each time examining…
Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and…
It is known that many classical inequalities linked to convolutions can be obtained by looking at the monotonicity in time of convolutions of powers of solutions to the heat equation, provided that both the exponents and the coefficients of…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…
We study nonequilibrium thermodynamics of complex information flows induced by interactions between multiple fluctuating systems. Characterizing nonequilibrium dynamics by causal networks (i.e., Bayesian networks), we obtain novel…
The Clausius inequality (CI) form of the second law of thermodynamics relates information changes (entropy) to changes in the first moment of the energy (heat and indirectly also work). Are there similar relations between other moments of…
Many fruitful analogies have emerged between the theories of quantum entanglement and thermodynamics, motivating the pursuit of an axiomatic description of entanglement akin to the laws of thermodynamics. A long-standing open problem has…
The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the…
We comment on a formulation of quantum statistical mechanics, which incorporates the statistical inference of Shannon. Our basic idea is to distinguish the dynamical entropy of von Neumann, $H = -k Tr \hat{\rho}\ln\hat{\rho}$, in terms of…
While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon's entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
We investigate how undecidability enters into computations of classical physical systems and contributes to the increase of entropy and loss of information. In actual computation with finite bit of information capacity we accept…
Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…
It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language to study a variety of…
Second law of thermodynamics can be apparently violated for systems whose dynamics depends on acquired information by measurement. However, when one consider measurement and erasure process together along with the system it saves the second…