2,217 research outputs found
The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons
This letter presents a new, solely thermodynamical argument for considering
the states of the quantum isolated horizon of a black hole as distinguishable.
We claim that only if the states are distinguishable, the thermodynamic entropy
is an extensive quantity and can be well-defined. To show this, we make a
comparison with a classical ideal gas system whose statistical description
makes only sense if an additional 1/N!-factor is included in the state counting
in order to cure the Gibbs paradox. The case of the statistical description of
a quantum isolated horizon is elaborated, to make the claim evident.Comment: 8 pages, closest to the published version; taken from the author's
diploma thesi
Nonlinear Stochastic Dynamics of Complex Systems, II: Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality
In this paper we revisit the notion of the "minus logarithm of stationary
probability" as a generalized potential in nonequilibrium systems and attempt
to illustrate its central role in an axiomatic approach to stochastic
nonequilibrium thermodynamics of complex systems. It is demonstrated that this
quantity arises naturally through both monotonicity results of Markov processes
and as the rate function when a stochastic process approaches a deterministic
limit. We then undertake a more detailed mathematical analysis of the
consequences of this quantity, culminating in a necessary and sufficient
condition for the criticality of stochastic systems. This condition is then
discussed in the context of recent results about criticality in biological
systemsComment: 28 page
Force balance in canonical ensembles of static granular packings
We investigate the role of local force balance in the transition from a
microcanonical ensemble of static granular packings, characterized by an
invariant stress, to a canonical ensemble. Packings in two dimensions admit a
reciprocal tiling, and a collective effect of force balance is that the area of
this tiling is also invariant in a microcanonical ensemble. We present
analytical relations between stress, tiling area and tiling area fluctuations,
and show that a canonical ensemble can be characterized by an intensive
thermodynamic parameter conjugate to one or the other. We test the equivalence
of different ensembles through the first canonical simulations of the force
network ensemble, a model system.Comment: 9 pages, 9 figures, submitted to JSTA
Psychophysical identity and free energy
An approach to implementing variational Bayesian inference in biological
systems is considered, under which the thermodynamic free energy of a system
directly encodes its variational free energy. In the case of the brain, this
assumption places constraints on the neuronal encoding of generative and
recognition densities, in particular requiring a stochastic population code.
The resulting relationship between thermodynamic and variational free energies
is prefigured in mind-brain identity theses in philosophy and in the Gestalt
hypothesis of psychophysical isomorphism.Comment: 22 pages; published as a research article on 8/5/2020 in Journal of
the Royal Society Interfac
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