Related papers: Physics of the Shannon Limits
The Gibbs paradox is a conventional paradox in classical statistical mechanics, typically resolved by invoking quantum indistinguishability through the 1/N! correction. In this letter, we present a resolution within classical ensemble…
Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon…
We prove the second law of thermodynamics and the nonequilibirum fluctuation theorem for pure quantum states.The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but…
A message of any sort can be regarded as a source of information. Claude. E. Shannon showed in the last century that information ("what we don't already know") is equivalent to the entropy as defined in statistical mechanics. A string of…
Drawing on an analogy with the second law of thermodynamics for adiabatically isolated systems, Cover argued that data-processing inequalities may be seen as second laws for "computationally isolated systems," namely, systems evolving…
We establish that entropy production, which is crucial to the characterization of thermodynamic irreversibility, is obtained through a variational principle involving the Kulback-Leibler divergence. A simple application of this…
We study the informational underpinnings of thermodynamics and statistical mechanics, using an abstract framework, general probabilistic theories, capable of describing arbitrary physical theories. This allows one to abstract the…
Thermodynamics and information have intricate inter-relations. The justification of the fact that information is physical, is done by inter-linking information and thermodynamics - through Landauer's principle. This modern approach towards…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
The first law of thermodynamics, which governs energy conservation, is traditionally formulated as an equality. Surprisingly, we demonstrate that the first law alone implies a universal Landauer-like inequality linking changes in system…
The association of information with entropy has been argued on plausibility arguments involving the operation of imaginary engines and beings, and it is not a universal theorem. In this paper, a theorem by Charles Bennett on reversible…
Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…
The standard formulation of thermostatistics, being based on the Boltzmann-Gibbs distribution and logarithmic Shannon entropy, describes idealized uncorrelated systems with extensive energies and short-range interactions. In this letter, we…
We use the formalism of 'Maximum Principle of Shannon's Entropy' to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order"…
The common saying, that information is power, takes a rigorous form in stochastic thermodynamics, where a quantitative equivalence between the two helps explain the paradox of Maxwell's demon in its ability to reduce entropy. In the present…
Materials that are constantly driven out of thermodynamic equilibrium, such as active and living systems, typically violate the Einstein relation. This may arise from active contributions to particle fluctuations which are unrelated to the…
We establish the fluctuation theorem in the presence of information exchange between a nonequilibrium system and other degrees of freedom such as an observer and a feedback controller, where the amount of information exchange is added to…
The second law of thermodynamics is discussed and reformulated from a quantum information theoretic perspective for open quantum systems using relative entropy. Specifically, the relative entropy of a quantum state with respect to…
We show that an information-theoretic property of Shannon's entropy power, known as concavity of entropy power, can be fruitfully employed to prove inequalities in sharp form. In particular, the concavity of entropy power implies the…
It is a common belief that in any environment where life is possible, life will be generated. Here it is suggested that the cause for a spontaneous generation of complex systems is probability driven processes. Based on equilibrium…