Related papers: Entropic probability and context states
We introduce a constructive framework for assigning thermodynamic structure to an arbitrary data system from its measured microstates. Starting from an empirical distribution over configurations, we first infer a data-driven energy function…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
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…
For time-dependent states generated by an external operation, a generalized free energy may be introduced by the relative entropy with respect to an equilibrium state realized after sufficient relaxation from the time-dependent states.…
We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic…
For sensory networks, we determine the rate with which they acquire information about the changing external conditions. Comparing this rate with the thermodynamic entropy production that quantifies the cost of maintaining the network, we…
Free energy and entropy are examined in detail from the standpoint of classical thermodynamics. The approach is logically based on the fact that thermodynamic work is mediated by thermal energy through the tendency for nonthermal energy to…
The entropy production of an open system coupled to a reservoir initialized in a canonical state can be expressed as a sum of two microscopic information-theoretic contributions: the system-bath mutual information and the relative entropy…
Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing…
Thermodynamics is based on the notions of energy and entropy. While energy is the elementary quantity governing physical dynamics, entropy is the fundamental concept in information theory. In this work, starting from first principles, we…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
Entropic dynamics, a program that aims at deriving the laws of physics from standard probabilistic and entropic rules for processing information, is developed further. We calculate the probability for an arbitrary path followed by a system…
Two identities in statistical mechanics involving entropy differences (or ratios of density of states) at constant energy are derived. The first provides a nontrivial extension of the Jarzynski equality to the microcanonical ensemble [C.…
We present quantitative relations between work and information that are valid both for finite sized and internally correlated systems as well in the thermodynamical limit. We suggest work extraction should be viewed as a game where the…
Several recent results on thermodynamics have been obtained using the tools of quantum information theory and resource theories. So far, the resource theories utilised to describe thermodynamics have assumed the existence of an infinite…
In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a…
Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…